351 lines
14 KiB
TypeScript
351 lines
14 KiB
TypeScript
import React, { useRef, useState, useEffect } from "react";
|
||
import { ArrowDown, Check, BookOpen, Layers } from "lucide-react";
|
||
import ParallelPerpendicularWidget from "../../../components/lessons/ParallelPerpendicularWidget";
|
||
import Quiz from "../../../components/lessons/Quiz";
|
||
import { LINEAR_PARALLEL_PERP_QUIZ_DATA } from "../../../utils/constants";
|
||
import { Frac } from "../../../components/Math";
|
||
|
||
interface LessonProps {
|
||
onFinish?: () => void;
|
||
}
|
||
|
||
const LinearParallelPerpendicularLesson: React.FC<LessonProps> = ({
|
||
onFinish,
|
||
}) => {
|
||
const [activeSection, setActiveSection] = useState(0);
|
||
const sectionsRef = useRef<(HTMLElement | null)[]>([]);
|
||
|
||
const scrollToSection = (index: number) => {
|
||
setActiveSection(index);
|
||
sectionsRef.current[index]?.scrollIntoView({
|
||
behavior: "smooth",
|
||
block: "start",
|
||
});
|
||
};
|
||
|
||
useEffect(() => {
|
||
const observer = new IntersectionObserver(
|
||
(entries) => {
|
||
entries.forEach((entry) => {
|
||
if (entry.isIntersecting) {
|
||
const index = sectionsRef.current.indexOf(
|
||
entry.target as HTMLElement,
|
||
);
|
||
if (index !== -1) setActiveSection(index);
|
||
}
|
||
});
|
||
},
|
||
{ rootMargin: "-20% 0px -60% 0px" },
|
||
);
|
||
sectionsRef.current.forEach((section) => {
|
||
if (section) observer.observe(section);
|
||
});
|
||
return () => observer.disconnect();
|
||
}, []);
|
||
|
||
const SectionMarker = ({
|
||
index,
|
||
title,
|
||
icon: Icon,
|
||
}: {
|
||
index: number;
|
||
title: string;
|
||
icon: any;
|
||
}) => {
|
||
const isActive = activeSection === index;
|
||
const isPast = activeSection > index;
|
||
return (
|
||
<button
|
||
onClick={() => scrollToSection(index)}
|
||
className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-blue-100" : "hover:bg-slate-100"}`}
|
||
>
|
||
<div
|
||
className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-blue-600 text-white" : isPast ? "bg-blue-400 text-white" : "bg-slate-200 text-slate-500"}`}
|
||
>
|
||
{isPast ? (
|
||
<Check className="w-4 h-4" />
|
||
) : (
|
||
<Icon className="w-4 h-4" />
|
||
)}
|
||
</div>
|
||
<div className="text-left">
|
||
<p
|
||
className={`text-sm font-bold ${isActive ? "text-blue-900" : "text-slate-600"}`}
|
||
>
|
||
{title}
|
||
</p>
|
||
</div>
|
||
</button>
|
||
);
|
||
};
|
||
|
||
return (
|
||
<div className="flex flex-col lg:flex-row min-h-screen">
|
||
<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 z-0 hidden lg:block">
|
||
<nav className="space-y-2">
|
||
<SectionMarker
|
||
index={0}
|
||
title="Parallel & Perpendicular"
|
||
icon={Layers}
|
||
/>
|
||
<SectionMarker index={1} title="Practice" icon={BookOpen} />
|
||
</nav>
|
||
</aside>
|
||
|
||
<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
|
||
{/* Section 1 */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[0] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
|
||
Parallel & Perpendicular Lines
|
||
</h2>
|
||
<div className="prose prose-slate text-lg text-slate-600 mb-8">
|
||
<p>
|
||
Parallel and perpendicular line questions appear on almost every
|
||
SAT. The core skill is: identify the slope of the given line,
|
||
apply the parallel or perpendicular slope rule, then write the new
|
||
equation through a given point.
|
||
</p>
|
||
</div>
|
||
|
||
<div className="bg-blue-50 border border-blue-200 rounded-2xl p-6 mb-8 space-y-5">
|
||
<h3 className="text-lg font-bold text-blue-900">
|
||
The Two Slope Rules
|
||
</h3>
|
||
|
||
<div className="grid md:grid-cols-2 gap-4">
|
||
<div className="bg-white rounded-xl p-5 border border-blue-100">
|
||
<p className="font-bold text-blue-900 mb-3 text-lg">
|
||
Parallel Lines
|
||
</p>
|
||
<div className="bg-blue-50 rounded-lg p-3 text-center mb-3">
|
||
<p className="font-mono text-blue-800 font-bold text-xl">
|
||
m₁ = m₂
|
||
</p>
|
||
<p className="text-xs text-slate-500 mt-1">
|
||
Same slope, different y-intercept
|
||
</p>
|
||
</div>
|
||
<ul className="text-slate-600 text-sm space-y-1 list-disc list-inside">
|
||
<li>Lines never intersect — they run side by side</li>
|
||
<li>Same slope guarantees they won't cross</li>
|
||
<li>
|
||
If y-intercepts also matched, the lines would be identical
|
||
</li>
|
||
</ul>
|
||
<div className="mt-3 bg-blue-50 rounded-lg p-2 font-mono text-xs text-slate-600">
|
||
y = 3x + 1 ∥ y = 3x − 7 (both slope = 3)
|
||
</div>
|
||
</div>
|
||
<div className="bg-white rounded-xl p-5 border border-blue-100">
|
||
<p className="font-bold text-indigo-900 mb-3 text-lg">
|
||
Perpendicular Lines
|
||
</p>
|
||
<div className="bg-indigo-50 rounded-lg p-3 text-center mb-3">
|
||
<p className="font-mono text-indigo-800 font-bold text-xl">
|
||
m₁ × m₂ = −1
|
||
</p>
|
||
<p className="text-xs text-slate-500 mt-1">
|
||
Negative reciprocal slopes
|
||
</p>
|
||
</div>
|
||
<ul className="text-slate-600 text-sm space-y-1 list-disc list-inside">
|
||
<li>Lines meet at a 90° angle</li>
|
||
<li>Rule: flip the fraction and change the sign</li>
|
||
<li>
|
||
A horizontal line (slope 0) is ⊥ to a vertical line
|
||
(undefined slope)
|
||
</li>
|
||
</ul>
|
||
<div className="mt-3 bg-indigo-50 rounded-lg p-2 font-mono text-xs text-slate-600">
|
||
y = <Frac n="2" d="3" />x + 1 ⊥ y = <Frac n="−3" d="2" />x + 5
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Negative Reciprocal Examples */}
|
||
<div className="bg-white rounded-xl p-5 border border-blue-100">
|
||
<p className="font-bold text-blue-800 mb-3">
|
||
Finding Perpendicular Slopes: Worked Examples
|
||
</p>
|
||
<div className="overflow-x-auto">
|
||
<table className="w-full text-sm border-collapse">
|
||
<thead>
|
||
<tr className="bg-blue-100 text-blue-900">
|
||
<th className="p-2 text-left font-bold">
|
||
Original Slope
|
||
</th>
|
||
<th className="p-2 text-left font-bold">
|
||
Step 1: Flip the fraction
|
||
</th>
|
||
<th className="p-2 text-left font-bold">
|
||
Step 2: Negate the sign
|
||
</th>
|
||
<th className="p-2 text-left font-bold">
|
||
Perpendicular Slope
|
||
</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody className="text-slate-600">
|
||
<tr className="border-b border-blue-50">
|
||
<td className="p-2 font-mono">2 (= 2÷1)</td>
|
||
<td className="p-2">
|
||
<Frac n="1" d="2" />
|
||
</td>
|
||
<td className="p-2">
|
||
<Frac n="−1" d="2" />
|
||
</td>
|
||
<td className="p-2 font-bold text-indigo-700">
|
||
<Frac n="−1" d="2" />
|
||
</td>
|
||
</tr>
|
||
<tr className="border-b border-blue-50 bg-slate-50">
|
||
<td className="p-2">
|
||
<Frac n="−3" d="4" />
|
||
</td>
|
||
<td className="p-2">
|
||
<Frac n="4" d="3" />
|
||
</td>
|
||
<td className="p-2">
|
||
<Frac n="4" d="3" />
|
||
</td>
|
||
<td className="p-2 font-bold text-indigo-700">
|
||
<Frac n="4" d="3" />
|
||
</td>
|
||
</tr>
|
||
<tr className="border-b border-blue-50">
|
||
<td className="p-2 font-mono">−5</td>
|
||
<td className="p-2">
|
||
<Frac n="1" d="5" /> (flip)
|
||
</td>
|
||
<td className="p-2">
|
||
<Frac n="1" d="5" /> (negate negative)
|
||
</td>
|
||
<td className="p-2 font-bold text-indigo-700">
|
||
<Frac n="1" d="5" />
|
||
</td>
|
||
</tr>
|
||
<tr className="bg-slate-50">
|
||
<td className="p-2 font-mono">0 (horizontal)</td>
|
||
<td className="p-2 font-mono">—</td>
|
||
<td className="p-2 font-mono">—</td>
|
||
<td className="p-2 font-bold text-indigo-700">
|
||
Undefined (vertical)
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</div>
|
||
|
||
{/* Full Problem Worked Examples */}
|
||
<div className="bg-white rounded-xl p-5 border border-blue-100">
|
||
<p className="font-bold text-blue-800 mb-3">
|
||
Complete Problem: Writing the Equation
|
||
</p>
|
||
<div className="space-y-4">
|
||
<div className="bg-blue-50 rounded-lg p-4 text-sm">
|
||
<p className="font-semibold text-blue-800 mb-2">
|
||
Example 1: Find the line parallel to y = 4x − 3 passing
|
||
through (2, 5)
|
||
</p>
|
||
<div className="font-mono space-y-1 text-slate-700">
|
||
<p>Parallel → same slope: m = 4</p>
|
||
<p>Use point-slope: y − 5 = 4(x − 2)</p>
|
||
<p>y − 5 = 4x − 8</p>
|
||
<p className="text-blue-700 font-bold">
|
||
y = 4x − 3 ← Wait, same as original! Confirm: passes
|
||
through (2, 5): 5 = 8 − 3 = 5 ✓
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div className="bg-indigo-50 rounded-lg p-4 text-sm">
|
||
<p className="font-semibold text-indigo-800 mb-2">
|
||
Example 2: Find the line perpendicular to 2x + 3y = 12
|
||
passing through (4, 1)
|
||
</p>
|
||
<div className="font-mono space-y-1 text-slate-700">
|
||
<p>
|
||
First, find slope of 2x + 3y = 12: y ={" "}
|
||
<Frac n="−2" d="3" />x + 4, so m = <Frac n="−2" d="3" />
|
||
</p>
|
||
<p>
|
||
Perpendicular slope: flip and negate → m ={" "}
|
||
<Frac n="3" d="2" />
|
||
</p>
|
||
<p>
|
||
Point-slope: y − 1 = <Frac n="3" d="2" />
|
||
(x − 4)
|
||
</p>
|
||
<p>
|
||
y = <Frac n="3" d="2" />x − 6 + 1
|
||
</p>
|
||
<p className="text-indigo-700 font-bold">
|
||
y = <Frac n="3" d="2" />x − 5
|
||
</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<div className="bg-red-50 border border-red-200 rounded-xl p-4 text-sm">
|
||
<p className="font-bold text-red-800 mb-1">
|
||
SAT Trap: Parallel Lines Must Have Different Intercepts
|
||
</p>
|
||
<p className="text-slate-700">
|
||
Parallel lines need the <em>same slope</em> but a{" "}
|
||
<em>different y-intercept</em>. If the intercepts also match,
|
||
the lines are identical — infinitely many intersections, not
|
||
parallel. The SAT sometimes includes a "same slope, same
|
||
intercept" option to trap students.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
<ParallelPerpendicularWidget />
|
||
|
||
<button
|
||
onClick={() => scrollToSection(1)}
|
||
className="mt-12 group flex items-center text-blue-600 font-bold hover:text-blue-800 transition-colors"
|
||
>
|
||
Next: Practice Quiz{" "}
|
||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||
</button>
|
||
</section>
|
||
|
||
{/* Section 2: Quiz */}
|
||
<section
|
||
ref={(el) => {
|
||
sectionsRef.current[1] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-8">
|
||
Practice Time
|
||
</h2>
|
||
{LINEAR_PARALLEL_PERP_QUIZ_DATA.map((quiz, idx) => (
|
||
<div key={quiz.id} className="mb-12">
|
||
<Quiz data={quiz} />
|
||
</div>
|
||
))}
|
||
<div className="p-8 bg-blue-900 rounded-2xl text-white text-center mt-12">
|
||
<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
|
||
<button
|
||
onClick={onFinish}
|
||
className="px-6 py-3 bg-white text-blue-900 font-bold rounded-full hover:bg-blue-50 transition-colors"
|
||
>
|
||
Finish Lesson ✓
|
||
</button>
|
||
</div>
|
||
</section>
|
||
</div>
|
||
</div>
|
||
);
|
||
};
|
||
|
||
export default LinearParallelPerpendicularLesson;
|