+476 DeMarco draws △PQR with vertices P(−4, 2), Q(2, 2), and R(2, −6). Then he dilates the triangle with a scale factor of 5 to create △P′Q′R′. How are the areas of the triangles related?
+9481 When you dilate the triangle, you increase two dimensions by 5.
The area will increase by 5 twice, that is 5*5 = 52 = 25
So, the area of △P′Q′R′ is 25 times bigger than the area of △PQR.
Here is an example:
△ABC has a base of 3 units and a height of 6 units.
It is dilated by a scale factor of 4.
△A'B'C' has a base of 3*4 units and a height of 6*4 units.
area of △ABC = (1/2)(3)(6) = 9
area of △A'B'C' = (1/2)(3*4)(6*4) = 9 * 4 * 4 = 9 * 42
The area of △A'B'C' is 42 times bigger than △ABC.
