Question

example 2
reflection in the x - or y - axis
triangle abc has coordinates a(3, 2), b(2, - 2), and c(4, - 5).
part a determine the coordinates of the vertices of the image after
a reflection in the x - axis.
predict graph the triangle. before performing
the reflection, predict your results.
the image of the triangle will be in the
and quadrants.
multiply the y - coordinate of each vertex by - 1.
find the coordinates of the vertices of the image.
(x,y)→(x, - y)
a(3,2)→a(3, - 2)
b(2, - 2)→b(
c(4, - 5)→c(

Explanation:

Step1: Predict quadrants

Original triangle has points in \(I\) ( \(A(3,2)\) ) and \(IV\) ( \(B(2, - 2)\), \(C(4,-5)\) ). After reflection in \(x -\)axis (\((x,y)\to(x, - y)\)), \(A(3,2)\to(3,-2)\) ( \(IV\) quadrant), \(B(2,-2)\to(2,2)\) ( \(I\) quadrant), \(C(4,-5)\to(4,5)\) ( \(I\) quadrant). So the image of the triangle will be in the \(I\) and \(IV\) quadrants.

Step2: Find coordinates of \(B'\)

For \(B(2,-2)\), using the rule \((x,y)\to(x, - y)\). Here \(x = 2\) and \(y=-2\), then \(-y=-(-2) = 2\). So \(B(2,-2)\to B'(2,2)\)

Step3: Find coordinates of \(C'\)

For \(C(4,-5)\), using the rule \((x,y)\to(x, - y)\). Here \(x = 4\) and \(y =-5\), then \(-y=-(-5)=5\). So \(C(4,-5)\to C'(4,5)\)

Answer:

The image of the triangle will be in the \(I\) and \(IV\) quadrants. \(B(2,-2)\to B'(2,2)\), \(C(4,-5)\to C'(4,5)\)