A figure has been dilated from the origin by a scale factor of of. If another dilation from the origin maps the dilated image back
onto the original figure, what is its scale factor?

See Explanation

Step-by-step explanation:

The question has missing details. So, I'll solve using a general assumption.

Let one of the coordinates of the figure be

Let the scale factor be n

When dilated, the new figure is:

To return the image back to the original figure, the new scale factor mus be a reciprocal of the previous scale factor i.e.

So:

Substitute n(x,y) for A';

Take for instance:

-- scale factor

To get A from A', using the analysis above

p> q if you calculate p is100 q is 79

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)