Find the midpoint: FM=5y+13, MG=5-3y I keep getting y=-1, and then putting it in but I'm just totally lost all I'm getting is 8 apparently and I'm not sure where …

Question

Find the midpoint:


`FM=5y+13, MG=5-3y`

I keep getting y=-1, and then putting it in but I'm just totally lost all I'm getting is 8 apparently and I'm not sure where to go next

Answer 1

FG = 16

Explanation:

Given:

• FM = 5y + 13
• MG = 5 - 3y
• M is the midpoint of FG

If M is the midpoint of FG then:

⇒ FM = MG

⇒ 5y + 13 = 5 - 3y

⇒ 5y + 13 + 3y = 5 - 3y + 3y

⇒ 8y + 13 = 5

⇒ 8y + 13 - 13 = 5 - 13

⇒ 8y = -8

⇒ y = -1

As M is the midpoint of FG then:

⇒ FG = FM + MG

⇒ FG = (5y + 13) + (5 - 3y)

⇒ FG = 5y + 13 + 5 - 3y

⇒ FG = 2y + 18

Substitute the found value of y into the found equation for FG:

⇒ FG = 2(-1) + 18

⇒ FG = -2 + 18

⇒ FG = 16