Question

If two lines are perpendicular which statement must be true

a. they have negative reciprocal slopes
b. they have the same slope
c. they have reciprocal slopes
d. they have oppsite slopes

Answer 1

A. They have negative reciprocal slopes

Answer 2

a. They have negative reciprocal slopes.

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=(2-1)/(3-1)=(1)/(2)`

Using slope formula :

m=
`(y_2-y_1)/(x_2-x_1)`

Slope of line CD,
`m_2=(-3+1)/(2-1)`

Slope of line
`,m_2=-2`

Slope of line AB,
`m_1=-(1)/(m_2)`

Slope of line AB,
`m_1=-(1)/(-2)=(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.