Question

The line passinf through which two ordered pairs would be perpendicular tp the equation y=4x-1 ?

Answer 1

(4, 2) and (8, 1) (option D)

Explanation:

The given equation:

y = 4x - 1

comparing with equation of line:

y = mx + c

m = slope = 4

c = y-intercept = -1

For a line to be perpendicular to another line, the slope of one line will be the negative reciprocal of the other line.

We need to find the option which will give a negative reciprocal of 4.

$slope=m\text{ = }\frac{y_2-y_1}{x_2-x_1}$

a) (1, -3) and (2, 1)

$\begin{gathered} slope=\text{ }\frac{1-(-3)}{2-1}=\frac{1+3}{1}\text{ = }\frac{\text{4}}{1} \\ \text{slope = 4} \end{gathered}$

b) (-4, 7) and (-1, -5)

$\begin{gathered} \text{slope = }\frac{-5-7}{-1-(-4)}=\frac{-5-7}{-1+4}=\frac{-12}{3} \\ \text{slope = -4} \end{gathered}$

c) (-8, -4) and (0, -2)

$\begin{gathered} \text{slope = }\frac{-2-(-4)}{0-(-8)}=\frac{-2+4}{0+8}=\text{ }\frac{2}{8} \\ \text{slope = }\frac{1}{4} \end{gathered}$

d) (4, 2) and (8, 1)

$\begin{gathered} \text{slope = }\frac{1-2}{8-4} \\ \text{slop}e\text{ }=\frac{-1}{4} \end{gathered}$

slope = 4

reciprocal of 4 = 1/4

negative reciprocal = - 1/4

Hence, the option whose slope gives the negative reciprocal of 4 is (4, 2) and (8, 1) (option D)