Question

1. what is the rule for reflecting a shape over the x - axis?

a. (x,y)→(-x,-y)
b. (x,y)→(y,x)
c. (x,y)→(-x,y)
d. (x,y)→(x,-y)

1. point a(9, - 4) is reflected over the y - axis. write the coordinates of a.

a. (-9,-4)
b. (9,-4)
c. (9,4)
d. (-9,4)

1. △abc has vertices a(-1,-2), b(-4,-4) and c

Explanation:

Step1: Recall the reflection rule over the x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So the rule is \((x,y)\to(x, - y)\).

Step2: Recall the reflection rule over the \(y\) - axis

When a point \((x,y)\) is reflected over the \(y\) - axis, the \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. For point \(A(9,-4)\) reflected over the \(y\) - axis, we have \(x = 9\) and \(y=-4\). Using the rule \((x,y)\to(-x,y)\), we substitute \(x = 9\) and \(y=-4\) into the formula. So \(A'\) has coordinates \((-9,-4)\).

Answer:

1. d. \((x,y)\to(x, - y)\)
2. a. \((-9,-4)\)