Answer:
(D): (-1,-6)
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-2,-5)[/tex]
[tex]m = -1[/tex]
Required
Find [tex](x_2,y_2)[/tex]
Slope (m) is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
Substitute values for m, x1 and x2
[tex]-1 = \frac{y_2 -(-5)}{x_2 - (-2)}[/tex]
[tex]-1 = \frac{y_2 +5}{x_2 +2}[/tex]
Cross Multiply:
[tex]-1(x_2 +2) = y_2 +5[/tex]
[tex]-x_2 -2 = y_2 +5[/tex]
Make y the subject
[tex]y_2 = -x_2 - 2 - 5[/tex]
[tex]y_2 = -x_2 - 7[/tex]
Only (D): (-1,-6) satisfy this condition:
Substitute -1 for x2 and -6 for y2.
[tex]-6 = -(-1) - 7[/tex]
[tex]-6 = 1- 7[/tex]
[tex]-6 =- 6[/tex]
Hence:
(D): (-1,-6) is true
