Question

A quadrilateral has vertices of (1,4), (7,3), (3,-5) and (8,-4). The quadrilateral is dilated by a scale factor of 3.5 with the origin as it's center. What are the coordinates of the vertices of the image of the quadrilateral?

Answer 1

`(3.5, 14),(24.5,10.5),(10.5,-17.5),(28,-14)`

Explanation:

Imagine drawing lines from some central point - in this case, the origin `(0,0)` - to each of the vertices. When we dilate the quadrilateral determined by these vertices, we're stretching those lines, those distances to the central point, by some given factor. In other words, the `x` and `y` coordinates of each vertex are getting scaled by the same give amount - in this case, 3.5.

When we perform the calculations on each of the vertices, we're left with these new ones:

`(1,4)->(3.5,14)`
`(7,3)->(24.5,10.5)`
`(3,-5)->(10.5,-17.5)`
`(8,-4)->(28,-14)`

Which form the vertices of our dilated quadrilateral.