Question

Square EFGH is drawn on a coordinate plane. Diagonal FH is on the line y − 3 = -1/3(x - 9). What is the slope of the diagonal GE?

a) 1
b) -1
c) 3
d) -3

Answer 1

The slope of diagonal GE of square EFGH is 3, as it is the negative reciprocal of the slope of diagonal FH, which is -1/3.

correct option is c) 3

Step-by-step explanation:

The student asked what the slope of the diagonal GE of square EFGH is, given that the diagonal FH is on the line with equation y - 3 = -1/3(x - 9). First, we need to recognize that the diagonals of a square are perpendicular to each other. The slope of diagonal FH given in the equation is -1/3, which is in the slope-intercept form y - y1 = m(x - x1).

Since the diagonals are perpendicular, the slope of GE will be the negative reciprocal of -1/3, which is 3.

Consequently, the slope of diagonal GE is determined to be 3, the negative reciprocal of the slope of FH. Understanding the interplay of slopes in perpendicular lines within geometric shapes provides a concise and insightful approach to solving problems related to the properties of squares and their diagonals.