Find the value of x or y that satisfies the given conditions

Question

The line containing (8,7) and (7, -6) is perpendicular to the line containing (2,4) and (x,3).

Answer 1

Find the value of x or y that satisfies the given conditions

The line containing (8,7) and (7, -6) is perpendicular to the line containing (2,4) and (x,3).

Key principle being taught/tested by this problem:

Perpendicular lines have slopes that are the opposite reciprocal of each other. That is, m and -1/m

The slope of the line containing (8,7) and (7,-6) is m = (-6-7)/(7-8) = (-13)/(-1) = 13

Therefore, the slope of the perpendicular line is -1/m = -1/13

So, -1/13 = (3-4)/(x-2)

(-1)*(x-2) = (-1)*13 [cross multiply)

x - 2 = 13

x = 15

When x=15, the given condition is satisfied.