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jarptica [38.1K]
3 years ago
12

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

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
7 0

The slopes of perpendicular lines are opposite reciprocals

The true statement is that segments FG and HJ are perpendicular

<h3>How to determine the relationship between the segments</h3>

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

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