Parallel Lines - High School Math

The line shown on the Cartesian coordinate graph below passes by points AB. Another line needs to be drawn parallel to line AB and passes by point C shown on the graph and point D.

What coordinates should point D have that will make line CD parallel to line AB?

a. (-3, 4)
b. (-5, 2)
c. (-6, 0)
d. (-9,-1)

Answer: The coordinates for point D are (-9,-1).

In order to solve this problem the student must recall that parallel lines have the same slope. Therefore, the slope that is calculated for line AB will be the same slope for the line parallel to it that passes through point C.

Therefore, step one is to calculate the slope for line AB.
The coordinates for point A are (6,1)
The coordinates for point B are (1,0)

The slope formula states that:

Let apply the formula to find the slope for line AB:

m = (0 - 4)/(1 – 6) = (- 4)/(- 5) = 4/5

An examination of point C on the graph reveals that the coordinates for this point are:
(- 4 , 3).

The student must now use this point and check each of the above coordinates provided as a possible answer to determine which pair resulted in a slope of 4/5.

Once the coordinate pair of (-9 , -1) is checked, it reveals the following:

m = (- 1 – 3)/ (- 9 – [- 4])
m = (- 1 – 3)/ (- 9 + 4) = (- 4)/(- 5) = 4/5

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