Question

2. Find the slope of GL, and BH using the coordinates; B(-4,3), G(-2, 4), H(1, -2), L(-1, -3). then determine if the lines are parallel.​

Answer 1

Given:

The coordinates of the points are B(-4,3), G(-2, 4), H(1, -2), L(-1, -3).

To find:

Whether GL and BH are parallel or not by using their slopes.

Solution:

If a line passes through the two points, then the slope of the line is

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

Using the slope formula, the slope of GL is

`m_1=(-3-4)/(-1-(-2))`

`m_1=(-7)/(-1+2)`

`m_1=(-7)/(1)`

`m_1=-7`

Using the slope formula, the slope of BH is

`m_2=(-2-3)/(1-(-4))`

`m_2=(-5)/(1+4)`

`m_2=(-5)/(5)`

`m_2=-1`

We know that slopes of parallel lines are always equal.

The slopes of GL and BH are -7 and -1 respectively but they are not equal, therefore GL and BH are not parallel lines.