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.
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