Question

use the figure shown to answer the following questions.

1. determine the coordinates of the image

△a′b′c′ after a reflection across the y - axis.
a′:(
,
) b′:(
,
) c′:(
,
)

Explanation:

Step1: Recall the rule for reflection across the y - axis

When a point \((x,y)\) is reflected across the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).

Step2: Find the coordinates of point \(A\)

From the graph, point \(A\) has coordinates \((4,7)\). Using the reflection rule \((x,y)\to(-x,y)\), for point \(A(4,7)\), \(x = 4\) and \(y=7\). After reflection, \(x\) becomes \(-4\) and \(y\) remains \(7\). So \(A'\) is \((- 4,7)\).

Step3: Find the coordinates of point \(B\)

From the graph, point \(B\) has coordinates \((1,8)\). Using the reflection rule \((x,y)\to(-x,y)\), for point \(B(1,8)\), \(x = 1\) and \(y = 8\). After reflection, \(x\) becomes \(-1\) and \(y\) remains \(8\). So \(B'\) is \((-1,8)\).

Step4: Find the coordinates of point \(C\)

From the graph, point \(C\) has coordinates \((2,2)\). Using the reflection rule \((x,y)\to(-x,y)\), for point \(C(2,2)\), \(x = 2\) and \(y=2\). After reflection, \(x\) becomes \(-2\) and \(y\) remains \(2\). So \(C'\) is \((-2,2)\).

Answer:

\(A':(-4,7)\), \(B':(-1,8)\), \(C':(-2,2)\)