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M is the midpoint of RT. RS=6x+7 and ST=9x-8. find the length of RS and RT

Sagot :

Akposevictoridn

Applying the definition of a midpoint of a segment, the lengths are:

RT = 74 units

RS = 37 units

What is the Midpoint of a Segment?

The midpoint is defined as the point that bisects a line segment into two equal halves.

If M is the midpoint of RT, therefore:

RS = ST

RS = 6x + 7

ST = 9x - 8

Substitute

6x + 7 = 9x - 8

6x - 9x = -7 - 8

-3x = -15

x = -15/-3

x = 5

RT = RS + ST [segment addition postulate]

RT = 6x + 7 + 9x - 8 [substitution]

RT = 15x - 1

Plug in the value of x

RT = 15(5) - 1

RT = 74 units

RS = 6x + 7 = 6(5) + 7

RS = 37 units.

Thus, applying the definition of a midpoint of a segment, the lengths are:

RT = 74 units

RS = 37 units

Learn more about the midpoint of a segment on:

https://brainly.com/question/7696289

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