A pair of points which is perpendicular to line L is: D. (3, -5),(-6, 3).
Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
For points A, we have:
[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-9)}\\\\Slope = \frac{9}{12}[/tex]
Slope = 9/12.
For points B, we have:
[tex]Slope = \frac{6\;-\;(-2)}{-6\;-\;(-9)}\\\\Slope = \frac{8}{-3}[/tex]
Slope = -8/3.
For points C, we have:
[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-5)}\\\\Slope = \frac{9}{8}[/tex]
Slope = 9/8.
For points D, we have:
[tex]Slope = \frac{3\;-\;(-5)}{-6\;-\;3}\\\\Slope = \frac{-8}{9}[/tex]
Slope = -8/9.
In Mathematics, the condition for perpendicularity of two lines is:
m₁ × m₂ = -1
9/8 × 8/9 = -1
Thus, points (3,−5) and (−6,3) are perpendicular to line L.
Read more on slope here: brainly.com/question/3493733
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Complete Question:
Line L has a slope of 9/8. The line through which of the following pair of points is perpendicular to L?
A. (−9,−6),(3,3)
B. (9,−2),(−6,6)
C. (−5,−6),(3,3)
D. (3,−5),(−6,3)
