Question

Given A(2, 3), B(8, 7), C(6, 1), which coordinate will make line AB perpendicular to line CD?

D(9, 3)
D(4, 4)
D(3, 3)
D(8, 4)​

Answer 1

The correct option is;

D(4, 4)

Explanation:

The given coordinates of the points are, A(2, 3) B(8, 7), C(6, 1), therefore, the coordinates of the point D that will make CD perpendicular to AB will have a slope = -1/m, where, m = the slope of the line segment AB

The formula for finding the slope, m, of a segment, given the coordinates of two points on the straight line segment (x₁, y₁), (x₂, y₂)

`Slope, \, m =(y_(2)-y_(1))/(x_(2)-x_(1))`

Therefore, for, the segment AB, we have;

m = (7 - 3)/(8 - 2) = 4/6 = 2/3

m = 2/3

Therefore, to make the segment AB perpendicular to the segment CD, the slope of the segment CD will be -1/m = -1/(2/3) = -3/2

The equation of the segment CD in point and slope form is therefore;

y - 1 = -3/2×(x - 6)

y - 1 = -3·x/2 + 9

The standard form of the equation of the segment CD is therefore;

y = -3·x/2 + 9 + 1 = -3·x/2 + 10

y = -3·x/2 + 10

The point that satisfies the above equation is the point (4, 4) because;

4 = -3 × 4/2 + 10

The correct option is therefore, D(4, 4).