Question

Given points F(3,1), G(5,2) H(2,4), and J(1,6)

Answer 1

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

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$FG = \frac{2 -1}{5 -3}$

$FG = \frac{1}{2}$

Also, we have:

$HJ = \frac{6 - 4}{1 - 2}$

$HJ = \frac{2}{-1}$

$HJ = -2$

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:

brainly.com/question/2531713