Question

Which best describes the relationship between the line that passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8)?A. same lineB. parallelC. neither perpendicular nor parallelD. perpendicular

Answer 1

Given the line which passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8).

To determine the relationship which best describes the line, the first thing we do is find the gradients of the lines.

For point A and B with coordinates:

`A(x_1,y_1),B(x_2,y_2)`
`\text{Gradient, m= }(y_2-y_1)/(x_2-x_1)`

For points (2, 3) and (5,8)

`\text{Gradient, m= }(8-3)/(5-2)=(5)/(3)`

For the points (-7, 5) and (-12, 8)

`\text{Gradient, m= }(8-5)/(-12-(-7))=(3)/(-5)=-(3)/(5)`

• Two lines are said to be ,parallel, ,if their gradients are the same.

,

• Two lines are said to be ,perpendicular ,if the ,product of the gradients is -1.

Product of the two gradients

`\begin{gathered} =(5)/(3)*-(3)/(5) \\ =-1 \end{gathered}`

Since the product of the gradients is -1, the two lines are said to be perpendicular.

The correct option is D