95.2k views
1 vote
3

6
A
8
9 10 11 12 13 14 15
>
Line p contains points (-4,-2) and (-6, 3). Which of the following pairs of points would be on a line perpendicular to line p?
(6,2) and (5,3)
(-4,3) and (-6,4)
O(-15,-1) and (-5,3)
(4,3) and (6,2)

1 Answer

5 votes

Final answer:

To find a line perpendicular to line p, we need to find a line with a slope that is the negative reciprocal of the slope of line p. The pair of points (-15,-1) and (-5,3) would be on a line perpendicular to line p.


Step-by-step explanation:

To find a line perpendicular to line p, we need to find a line with a slope that is the negative reciprocal of the slope of line p. The slope of line p can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on line p.

Slope of line p = (3 - (-2)) / (-6 - (-4)) = 5 / (-2) = -2.5

The negative reciprocal of -2.5 is positive 0.4. Therefore, any line perpendicular to line p will have a slope of 0.4.

Let's check which pair of points has a slope of 0.4. Using the formula again:

Slope of pair (6,2) and (5,3) = (3 - 2) / (5 - 6) = 1 / -1 = -1

Slope of pair (-4,3) and (-6,4) = (4 - 3) / (-6 - (-4)) = 1 / -2 = -0.5

Slope of pair (-15,-1) and (-5,3) = (3 - (-1)) / (-5 - (-15)) = 4 / 10 = 0.4

Slope of pair (4,3) and (6,2) = (2 - 3) / (6 - 4) = -1 / 2 = -0.5

Therefore, the pair of points (-15,-1) and (-5,3) would be on a line perpendicular to line p.


Learn more about Geometry

User Matt Polito
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.