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

Answer:

Option (2)

Step-by-step 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 = $\frac{y_2-y_1}{x_2-x_1}$

                              = $\frac{1+2}{10-1}$

                              = $\frac{3}{9}$

                         m₁ = $\frac{1}{3}$

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

Slope of the line 2 = $\frac{y_2-y_1}{x_2-x_1}$

                               = $\frac{8+4}{-2-2}$

                               = $-\frac{12}{4}$

                         m₂ = -3

Since, m₁ × m₂ = $\frac{1}{3}\times (-3)$

                        = (-1)

Therefore, given lines are perpendicular to each other.

Option (2) is the correct option.