Question

example 3 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.

multiply the y - coordinate of each vertex by - 1.
find the coordinates of the vertices of the image.
$(x,y)\to(x, - y)$
$a(3,2)\to a(3, - 2)$
$b(2, - 2)\to b(\\_,\\_)$
$c(4, - 5)\to c(\\_,\\_)$
check the image matches the prediction.

part b reflect $\triangle abc$ in the y - axis. determine the coordinates of
the image.
predict before performing the reflection, predict your results.

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: Reflection in the x - axis

For a reflection in the x - axis, the rule is \((x,y)\to(x, - y)\).
For point \(B(2,-2)\), applying the rule: \(x = 2\), \(y=-2\), so \(B'\) has coordinates \((2,2)\) (since \(-y=-(-2) = 2\)).
For point \(C(4,-5)\), applying the rule: \(x = 4\), \(y = - 5\), so \(C'\) has coordinates \((4,5)\) (since \(-y=-(-5)=5\)).

Step2: Reflection in the y - axis

For a reflection in the y - axis, the rule is \((x,y)\to(-x,y)\).
For point \(A(3,2)\), applying the rule: \(x = 3\), so \(-x=-3\), and \(A'\) has coordinates \((-3,2)\).
For point \(B(2,-2)\), applying the rule: \(x = 2\), so \(-x=-2\), and \(B'\) has coordinates \((-2,-2)\).
For point \(C(4,-5)\), applying the rule: \(x = 4\), so \(-x=-4\), and \(C'\) has coordinates \((-4,-5)\).

Answer:

• Part A: \(B'(2,2)\), \(C'(4,5)\)
• Part B: \(A'(-3,2)\), \(B'(-2,-2)\), \(C'(-4,-5)\)