Question

Find the equation of the line passing through point (4,2) and perpendicular to AB

Answer 1

a. -⅓

b. 3

c. y = 3x - 10

Explanation:

a. Gradient of line AB:

A(1, 3), B(7, 1)

`Gradient = (y_2 - y_1)/(x_2 - x_1) = (1 - 3)/(7 - 1) = (-2)/(6) = -(1)/(3)`

Gradient (m) = -⅓

b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.

Thus, the negative reciprocal of -⅓ = 3

Gradient of the line perpendicular to line AB = 3

c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:

We can write the equation using the point-slope form equation, y - b = m(x - a), where,

(a, b) represents a point on the line, and,

m = gradient/slope

We know that the gradient/slope (m) = 3

Also, a point, (a, b) = (4, 2).

Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)

Thus:

y - 2 = 3(x - 4)

y - 2 = 3x - 12

Add 2 to both sides

y = 3x - 12 + 2

y = 3x - 10