Chapter 4, Problem 18RP

To determine

To Verify: H can Have (9, 6) as coordinates or not.

Explanation of Solution

Given information: coordinates of E and F are (2, 7) and (4, 3).

Formula Used: Slope of the line joining (x₁, y1) and (x₂, y2) is $\frac{y_2-y_1}{x_2-x_1}$

If two lies are perpendicular then product of their slops is -1.

Calculation:

Slope of $EF=\frac{3-7}{4-2}=-2$

  $\therefore$ Slope of any line perpendicular to EF must be $\frac{1}{2}$ .

Slope of line joining F(4,3) and (9,6) is

  $M=\frac{6-3}{9-4}=\frac{3}{5}.$

Hence H cannot have coordinates (9, 6).