Question

Ryan buys an 8 foot long by 6 foot wide piece of fabric. He wants to cut a smaller, similar rectangular piece that has a scale factor of k = 1/4. If point A(-4,3) is the top left hand vertex of both original piece of fabric and the piece Ryan wishes to cut out, what are the coordinates of the vertices for the piece Ryan will cut?

Answer 1

The smaller rectangular piece Ryan cuts from an 8x6 fabric, with a scale factor of 1/4, has a top-left vertex at A'(-2, 4.5) compared to A(-4, 3).

Ryan's original piece of fabric is 8 feet long and 6 feet wide. The scale factor for the smaller, similar rectangular piece he wants to cut is k = 1/4. To find the dimensions of the smaller piece, we multiply the dimensions of the original piece by the scale factor.

The length of the smaller piece will be 8 * (1/4) = 2 feet, and the width will be 6 * (1/4) = 1.5 feet.

Now, let's consider the coordinates of the top-left vertex A(-4,3) for both pieces. Since the scale factor applies uniformly to all dimensions, we can use it to find the new coordinates. The x-coordinate will be shifted by 8 * (1/4) = 2 units, and the y-coordinate will be shifted by 6 * (1/4) = 1.5 units.

Therefore, the coordinates of the top-left vertex for the smaller piece will be A'(-2, 4.5).