Question

In the graph below, line k with equation y = -k makes a 45° angle with the x- and y- axes. Complete the following: R k R y : (2,5), 1. (5, -2) 2. (-5, -2) 3. (-5, 2)

Answer 1

1.The value of k is -5.

2. Rk is (5, -5).

3. Ry is (-5, 5).

Explanation:

In the graph, line k with equation y = -k makes a 45° angle with the x- and y-axes. We need to find the values of k, Rk, and Ry given the point (2,5).

To find the value of k, we can substitute the coordinates (2,5) into the equation y = -k and solve for k.

Substituting the x-coordinate (2) and the y-coordinate (5) into the equation, we get:

5 = -k

Solving for k, we find that k = -5.

Therefore, the value of k is -5.

Now, to find Rk and Ry, we can use the given equation y = -k and substitute different x-values to find the corresponding y-values.

Using x = 5:

y = -(-5) = 5

Therefore, Rk is (5, -5).

Using x = -5:

y = -(-5) = 5

Therefore, Ry is (-5, 5).