Question

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

Explanation:

Step1: Determine quadrants

Original triangle is in Quadrants I and IV. When reflected over \(y -\)axis, image will be in Quadrants II and III.

Step2: Calculate \(A'\)

For \(A(3,2)\), using \((x,y)\to(-x,y)\), \(x = 3\), so \(A'\) has \(x=-3\), \(A'(-3,2)\)

Step3: Calculate \(B'\)

For \(B(2, - 2)\), using \((x,y)\to(-x,y)\), \(x = 2\), so \(B'\) has \(x=-2\), \(B'(-2,-2)\)

Step4: Calculate \(C'\)

For \(C(4,-5)\), using \((x,y)\to(-x,y)\), \(x = 4\), so \(C'\) has \(x=-4\), \(C'(-4,-5)\)

Answer:

The image of the triangle will be in the \(II\) and \(III\) quadrants. \(A'(-3,2)\), \(B'(-2,-2)\), \(C'(-4,-5)\)