Question

question 6 points 4
the vertices of triangle abc are (2, 1), (-2, 4), and (4, -2). if the triangle is reflected across the x-axis, then find the coordinates of the reflected triangle.

Explanation:

Step1: Recall reflection rule over x - axis

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So, the new coordinates \((x',y')\) after reflection across the \(x\) - axis are given by \(x'=x\) and \(y'=-y\).

Step2: Reflect point \(A(2,1)\)

For point \(A=(2,1)\), using the reflection rule: \(x = 2\), \(y = 1\). Then \(x'=2\) and \(y'=- 1\). So, the reflected point \(A'\) is \((2,-1)\).

Step3: Reflect point \(B(-2,4)\)

For point \(B = (-2,4)\), using the reflection rule: \(x=-2\), \(y = 4\). Then \(x'=-2\) and \(y'=-4\). So, the reflected point \(B'\) is \((-2,-4)\).

Step4: Reflect point \(C(4,-2)\)

For point \(C=(4,-2)\), using the reflection rule: \(x = 4\), \(y=-2\). Then \(x' = 4\) and \(y'=-(-2)=2\). So, the reflected point \(C'\) is \((4,2)\).

Answer:

The coordinates of the reflected triangle's vertices are \(A'(2,-1)\), \(B'(-2,-4)\) and \(C'(4,2)\)