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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.​

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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.

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