To determine the slope of diagonal FH in the square EFGH, given that diagonal GE is on the line [tex]\( y - 3 = 3(x + 4) \)[/tex], we start with these steps:
1. Identify the slope of diagonal GE:
- The equation of the line can be rewritten in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope.
- Starting with the given equation [tex]\( y - 3 = 3(x + 4) \)[/tex], let's simplify it:
[tex]\[
y - 3 = 3(x + 4)
\][/tex]
Distribute the 3 on the right side:
[tex]\[
y - 3 = 3x + 12
\][/tex]
Add 3 to both sides to isolate [tex]\( y \)[/tex]:
[tex]\[
y = 3x + 15
\][/tex]
- From this equation, it is clear that the slope [tex]\( m \)[/tex] of the line (and therefore the slope of diagonal GE) is 3.
2. Determine the relationship between the slopes of the diagonals in a square:
- For a square, the diagonals are perpendicular to each other. The product of the slopes of two perpendicular lines is -1.
- Thus, if the slope of diagonal GE is 3, the slope of diagonal FH is the negative reciprocal of 3.
3. Calculate the slope of diagonal FH:
- The negative reciprocal of 3 is:
[tex]\[
-\frac{1}{3}
\][/tex]
Therefore, the slope of diagonal FH is [tex]\(-\frac{1}{3}\)[/tex]. The correct answer to the question is:
[tex]\[
-\frac{1}{3}
\][/tex]
