Question

Enter the slope-intercept equation for the image of line ℓ after a clockwise rotation of 90°. (Hint: To find the image of line ℓ, choose two or more points on the line and find the images of the points.)

Answer 1

Answer:

$y=\frac{1}{7}x-\frac{6}{7}$

Step-by-step explanation:

Two points (1, -1) and (0, 6) are lying on the given line.

Rule to find the coordinates of a point by the rotation of 90° clockwise is,

(x, y) → (y, -x)

Therefore, image points of (1, -1) and (0, 6) will be,

(1, -1) → (-1, -1)

(0, 6) → (6, 0)

Slope of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

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

Therefore, slope of the line passing through (-1, -1) and (6, 0) will be,

m = $\frac{0+1}{6+1}$ = $\frac{1}{7}$

Equation of the line passing through (6, 0) and slope = $\frac{1}{7}$

y - y' = m(x - x')

y - 0 = $\frac{1}{7}(x - 6)$

$y=\frac{1}{7}x-\frac{6}{7}$