Question

If two lines are perpendicular which statement must be true

Answer 1

A. They have negative reciprocal slopes

Answer 2

Answer:

a. They have negative reciprocal slopes.

Step-by-step explanation:

When two lines are perpendicular then slopes of two perpendicular lines are opposite reciprocal.

For example, we take two lines one line passing through the points A(2}{,1) and B(3,2) and another line passing through the points C(1,-1) and D(2,-3)

The slope of line AB ,$m_1=\frac{2-1}{3-1}=\frac{1}{2}$

Using slope formula :

m=$\frac{y_2-y_1}{x_2-x_1}$

Slope of line CD,$m_2=\frac{-3+1}{2-1}$

Slope of line $,m_2=-2$

Slope of line AB,$m_1=-\frac{1}{m_2}$

Slope of line AB,$m_1=-\frac{1}{-2}=\frac{1}{2}$

Hence, Slopes of two lines AB and CD are opposite reciprocals. Therefore,the lines AB and CD are perpendicular.

Answer :a. They have negative reciprocal slopes.