Question

Point H is the midpoint of FG. What is the value of y? G(4x, 6y + 6) H(4, 15) F(2y + 2, 2x + 4)
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Answer 1

Answer:

  y = 3.4

Step-by-step explanation:

You want to find the value of y, given the end points of segment FG and midpoint H(4, 15), and end point expressions G(4x, 6y+6) and F(2y+2, 2x+4).

Setup

The midpoint coordinates are the average of the end point coordinates:

  (F +G)/2 = H

  ((2y +2, 2x +4) +(4x, 6y +6))/2 = (4, 15)

Simplifying, we have ...

  (4x +2y +2, 2x +6y +10)/2 = (4, 15)

  (2x +y +1, x +3y +5) = (4, 15)

Solution

Subtracting the coordinates on the right, we can write these as separate equations in general form:

• 2x +y -3 = 0
• x +3y -10 = 0

Using the first equation, we can write an expression for y that can be substituted into the second equation.

  y = 3 -2x . . . . . expression for y

  x +3(3 -2x) -10 = 0 . . . . substitute for y

  -5x -1 = 0 . . . . . . . collect terms

  x +0.2 = 0 . . . . . . divide by -5

  x = -0.2 . . . . . . . . subtract 0.2

  y = 3 -2(-0.2) = 3.4 . . . . find y

The solution to the system of equations is (x, y) = (-0.2, 3.4).

The value of y is 3.4.

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Additional comment

As noted above, x=-0.2, so the end points are ...

  F = (2(3.4) +2, 2(-0.2) +4) = (8.8, 3.6)

  G = (4(-0.2), 6(3.4) +6) = (-0.8, 26.4)