Question

Determine which of the following lines, if any, are perpendicular • Line A passes through (2,7) and (-1,10) • Line B passes through (-4,7) and (-1,6)• Line C passed through (6,5) and (7,9)

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

Line A:

point 1 (2,7)

point 2 (-1,10)

Line B:

point 1 (-4,7)

point 2 (-1,6)

Line C:

point 1 (6,5)

point 2 (7,9)

Step 02:

perpendicular lines:

slope of the perpendicular line, m’

m' = - 1 / m

Line A:

slope:

`m\text{ = }(y2-y1)/(x2-x1)=(10-7)/(-1-2)=(3)/(-3)=-1`

Line B:

slope:

`m=(y2-y1)/(x2-x1)=(6-7)/(-1-(-4))=(-1)/(-1+4)=(-1)/(3)`

Line C:

slope:

`m\text{ = }(y2-y1)/(x2-x1)=(9-5)/(7-6)=(4)/(1)=4`

m' = - 1 / m ===> none of the slopes meet the condition

The answer is:

there are no perpendicular lines