Question

Given A(-1,4), B(2,-5), and C(3, 4), which coordinate pair will make AB perpendicular to CD ?

Answer 1

Answer:

The coordinate pair of the point D that will make AB perpendicular to CD is the D(6, 3)

Step-by-step explanation:

The slope of the given line AB can be presented as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m =\dfrac{-5-4}{2-(-1)} = \dfrac{-9}{3} =-3$

The slope of a perpendicular line  to a given line is equal to the negative reciprocal of the slope of the given line

Therefore, the slope of the perpendicular to a line that has a slope of m is -1/m

The slope of the perpendicular to the line AB is therefore $-\dfrac{1}{3}$

From which we get the equation of the perpendicular to the line AB given as follows;

y - 4 = -1/3 × (x - 3)

y - 4 = -x/3 + 1

y = -x/3 + 1 + 4

y = -x/3 + 5

When x = 6, y = -6/3 + 5 = 3

Therefore, the coordinate pair of the point D that will make AB perpendicular to CD is the D(6, 3).