Question

Line e passes through points (9, 9) and (1, 4). Line f passes through points (1, 5) and (9, 10). Are line e and line f parallel or perpendicular?

Answer 1

Let A(9, 9) & B(1, 4) are two point through which Line e passes.

Equation of e is given by

y - y1 = y2 - y1/ x2 - x1(x - x1)

or, y - 9 = 4-9/1-9 (x - 9)

or, -8y + 72 = -5x + 45

or, 5x - 8y + 27 = 0...........1.

Again,

consider C (1, 5) & D (9, 10) are other two points through with Line f pass through.

Also, eqn of f is,

y- 5 = 10-5/9-1 (x - 1)

or, 8y - 5 = 5x - 5

or, 5x - 8y =0 ...........2.

Let m1 and m2 are slopes between the lines.

Now, slope of 1. = - coef. of x/ coef. of y

= -5/-8 = 5/8 =m1

& slope of 2. = -5/-8 = 5/8 = m2

Since slopes of lines i. e. m1 = m2, so the lines are parallel to each other.