The slopes of perpendicular lines are opposite reciprocals
The true statement is that segments FG and HJ are perpendicular
How to determine the relationship between the segments
The coordinates of the points are given as:
F = (3,1)
G = (5,2)
H = (2,4)
J = (1,6)
Start by calculating the slopes of FG and HJ using the following slope formula
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]FG = \frac{2 -1}{5 -3}[/tex]
[tex]FG = \frac{1}{2}[/tex]
Also, we have:
[tex]HJ = \frac{6 - 4}{1 - 2}[/tex]
[tex]HJ = \frac{2}{-1}[/tex]
[tex]HJ = -2[/tex]
To determine the relationship, we make use of the following highlights
- Parallel lines have the same slope
- The slopes of perpendicular lines are opposite reciprocals
From the computation above, we have:
- The slopes of both lines are not equal
- The slopes are opposite reciprocals i.e. 2 = -1(-1/2)
Hence, segment FG and HJ are perpendicular
Read more about perpendicular lines at:
https://brainly.com/question/2531713
