Option D: 3 is the slope of the diagonal GE
Explanation:
Given that EFGH is a square drawn on a coordinate plane.
Diagonal FH is on the line [tex]y-3=-\frac{1}{3} (x+9)[/tex]
We need to determine the slope of the diagonal GE.
Since, EFGH is a square and FH and GE are diagonals of the square.
The diagonals FH and GE are perpendicular to each other.
Thus, the slope of GE can be determined using the formula,
[tex]m_1\cdot m_2=-1[/tex]
where [tex]m_1[/tex] is the slope of FH and [tex]m_2[/tex] is the slope of GE
From the line [tex]y-3=-\frac{1}{3} (x+9)[/tex] , the slope is given by
[tex]m_1=-\frac{1}{3}[/tex]
Let us substitute the slope [tex]m_1=-\frac{1}{3}[/tex] in the formula, we get,
[tex]-\frac{1}{3} \cdot m_2=-1[/tex]
Multiplying both sides by [tex]-\frac{1}{3}[/tex] , we have,
[tex]m_2=3[/tex]
Thus, the slope of the diagonal GE is 3
Therefore, Option D is the correct answer.
