Lucy draws a line on a coordinate plane. which transformation will always result in a line perpendicular to lucy’s line? question 1 options: reflect over the x -axis, and then reflect over the y -axis rotate 270° clockwise around the origin dilate by a factor of 2 with the origin as the center of dilation reflect over the line y = x

Lucy draws a line on a coordinate plane. We have to identify the transformation which will always result in a line perpendicular to Lucy’s line.

Referring to the given options.

By rotating 270 degrees clockwise around the origin, Lucy will get a line perpendicular to the Lucy's line. As, when we rotate 270 degrees clockwise about the origin, we multiplies the x coordinate by '-1' and interchanges the x and y coordinate, which gives the line which is always perpendicular to the Lucy's given line.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)