Question

what are the coordinates of the image of vertex f after a reflection across the line y = -x? (-1, -3) (3, -1) (1, 3) (-3, 1) g(-2, -3) f(1, -3) e(-1, -5) h(2, -5)

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the line $y = -x$ is $(x,y)\to(-y,-x)$.

Step2: Identify original coordinates

The coordinates of vertex F are $(1,-3)$.

Step3: Apply the rule

For the point $(1,-3)$, when we apply the rule $(x,y)\to(-y,-x)$, we substitute $x = 1$ and $y=-3$. So, $-y=-(-3) = 3$ and $-x=-1$. The new - coordinates are $(3,-1)$.

Answer:

$(3,-1)$