Question

triangle xyz is reflected across the x - axis. the result is △xyz, as shown below. (a) the arrows below show that the coordinates on the left are mapped to the coordinates on the right. fill in the blanks to give the coordinates after the reflection. original coordinates → final coordinates x(-7,3) → x( , ) y(5,9) → y( , ) z(6,3) → z( , )

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected across the $x -$axis, the $x$-coordinate remains the same and the $y$-coordinate changes its sign. That is, $(x,y)\to(x, - y)$.

Step2: Find $X'$ coordinates

For point $X(-7,3)$, applying the reflection rule $(x,y)\to(x, - y)$, we get $X'(-7,-3)$.

Step3: Find $Y'$ coordinates

For point $Y(5,9)$, applying the reflection rule $(x,y)\to(x, - y)$, we get $Y'(5,-9)$.

Step4: Find $Z'$ coordinates

For point $Z(6,3)$, applying the reflection rule $(x,y)\to(x, - y)$, we get $Z'(6,-3)$.

Answer:

$X'(-7,-3)$
$Y'(5,-9)$
$Z'(6,-3)$