Question

triangle def is reflected across the line y = x. the result is △def, 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 d(-2, -4) → d(,) e(6, 1) → e(,) f(3, -9) → f(,)

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the line $y = x$, the coordinates are swapped, so the new point is $(y,x)$.

Step2: Find $D'$

For point $D(-2,-4)$, after reflection across $y = x$, we swap the coordinates. So $D'$ is $(-4,-2)$.

Step3: Find $E'$

For point $E(6,1)$, after reflection across $y = x$, we swap the coordinates. So $E'$ is $(1,6)$.

Step4: Find $F'$

For point $F(3,-9)$, after reflection across $y = x$, we swap the coordinates. So $F'$ is $(-9,3)$.

Answer:

$D'(-4,-2)$
$E'(1,6)$
$F'(-9,3)$