Question

△abc is reflected about the line y = -x to give △abc with vertices a(-1, 1), b(-2, -1), c(-1, 0). what are the vertices of △abc?
○ a. a(1, -1), b(-1, -2), c(0, -1)
○ b. a(-1, 1), b(1, 2), c(0, 1)
○ c. a(-1, -1), b(-2, -1), c(-1, 0)
○ d. a(1, 1), b(2, -1), c(1, 0)
○ e. a(1, 2), b(-1, 1), c(0, 1)

Explanation:

Step1: Recall the reflection rule

When a point \((x,y)\) is reflected about the line \(y = -x\), the transformation rule is \((x,y)\to(-y,-x)\). To get the original point from the reflected point, we use the reverse rule: if \((x',y')\) is the reflected - point, then the original point \((x,y)\) satisfies \(x=-y'\) and \(y = -x'\).

Step2: Find the coordinates of \(A\)

For \(A'(-1,1)\), using \(x=-y'\) and \(y=-x'\), we have \(x=-1\) (since \(y' = 1\)) and \(y = 1\) (since \(x'=-1\)). So the original \(A\) has coordinates \((1, - 1)\).

Step3: Find the coordinates of \(B\)

For \(B'(-2,-1)\), using \(x=-y'\) and \(y=-x'\). Here \(y'=-1\), so \(x = 1\); \(x'=-2\), so \(y = 2\). So the original \(B\) has coordinates \((-1,-2)\).

Step4: Find the coordinates of \(C\)

For \(C'(-1,0)\), using \(x=-y'\) and \(y=-x'\). Since \(y' = 0\), \(x=0\); since \(x'=-1\), \(y = 1\). So the original \(C\) has coordinates \((0,-1)\).

Answer:

A. \(A(1, - 1),B(-1,-2),C(0,-1)\)