Question

1. point c is the image of c under a reflection across the y - axis. find the coordinates of c.

c(7, -15)

1. point p is the image of p under a reflection across the y = x. find the coordinates of p.

p(12.5, 31.5)

1. point h is the image of h under a reflection across the y = -1. find the coordinates of h.

h(6, -9)

Explanation:

Step1: Reflect C over y-axis

For a point $(x,y)$, reflection over y-axis is $(-x,y)$.
For $C(7, -15)$: $C' = (-7, -15)$

Step2: Reflect P over $y=x$

For a point $(x,y)$, reflection over $y=x$ is $(y,x)$.
For $P(12.5, 31.5)$: $P' = (31.5, 12.5)$

Step3: Reflect H over $y=-1$

First, calculate vertical distance from $y$-coordinate to $y=-1$: $|-9 - (-1)| = |-8| = 8$.
Add twice this distance to original $y$-coordinate: $-9 + 2\times8 = -9 + 16 = 7$.
$x$-coordinate stays the same, so $H' = (6, 7)$

Answer:

1. $C'(-7, -15)$
2. $P'(31.5, 12.5)$
3. $H'(6, 7)$