Question

1. use the given diagram. eh is the perpendicular bisector of df. use the values of x and y to find the measure of fh.

a. 31
b. 32
c. 36
d. 44

Explanation:

Step1: Find x from EH and ED

Since EH is the perpendicular bisector, EH = ED? Wait, no, EH is perpendicular bisector of DF, so H is midpoint, and EF = ED? Wait, looking at the diagram, EH is perpendicular bisector of DF, so EF = ED (since any point on perpendicular bisector is equidistant from endpoints). So \( 7x + 9 = 9x - 1 \).
Solve for x: \( 9 + 1 = 9x - 7x \) → \( 10 = 2x \) → \( x = 5 \).

Step2: Find y from FG and DG

Also, since EH is perpendicular bisector, and FG and DG are marked equal? Wait, FG is \( 7y + 8 \), DG is \( 10y - 4 \). So \( 7y + 8 = 10y - 4 \).
Solve for y: \( 8 + 4 = 10y - 7y \) → \( 12 = 3y \) → \( y = 4 \).

Step3: Calculate FH

FH is \( 3x + 4y \). Substitute x = 5, y = 4: \( 3(5) + 4(4) = 15 + 16 = 31 \)? Wait, no, wait: Wait, maybe I mixed up. Wait, EH is perpendicular bisector of DF, so FH = DH? Wait, no, the expression for FH is \( 3x + 4y \). Let's check again.

Wait, x = 5, y = 4. So 3x + 4y = 15 + 16 = 31. But let's verify. Wait, EF = 7x + 9 = 7*5 +9= 35 +9=44. ED = 9x -1=45 -1=44. Correct. FG=7y +8=28 +8=36. DG=10y -4=40 -4=36. Correct. Then FH=3x +4y=15 +16=31. So the answer is 31, which is option A.

Answer:

A. 31