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

`y=(1)/(7)x-(6)/(7)`

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 =
`(y_2-y_1)/(x_2-x_1)`

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

m =
`(0+1)/(6+1)` =
`(1)/(7)`

Equation of the line passing through (6, 0) and slope =
`(1)/(7)`

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

y - 0 =
`(1)/(7)(x - 6)`

`y=(1)/(7)x-(6)/(7)`