Question

Given below are descriptions of two lines. Line 1: Goes through (-2,10) and (1,1) Line 2: Goes through (-2,8) and (2,-4)

Answer 1

Option (2)

Explanation:

1). If two lines have the same slope, lines are defined as parallel.

m₁ = m₂

2). If the multiplication of the slopes of two lines is (-1), lines will be perpendicular.

m₁ × m₂ = (-1)

Line 1 : It passes through two points (-2, 10) and (1, 1).

Slope of the line 1 =
`(y_2-y_1)/(x_2-x_1)`

=
`(1+2)/(10-1)`

=
`(3)/(9)`

m₁ =
`(1)/(3)`

Line 2 : It passes through two points (-2, 8) and (2, -4).

Slope of the line 2 =
`(y_2-y_1)/(x_2-x_1)`

=
`(8+4)/(-2-2)`

=
`-(12)/(4)`

m₂ = -3

Since, m₁ × m₂ =
`(1)/(3)* (-3)`

= (-1)

Therefore, given lines are perpendicular to each other.

Option (2) is the correct option.