Polygon ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to create polygon A′B′C′D′. If the endpoints of are located at (0, -7) and (8, 8), what is the length of ? Use the distance formula to help you decide:
To find the length of a line segment, we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Given the endpoints of the line segment , we have the following coordinates:
A (0, -7) and B (8, 8).
Now, let's substitute the coordinates into the distance formula and calculate the length of :
d = √((8 - 0)^2 + (8 - (-7))^2)
= √(8^2 + 15^2)
= √(64 + 225)
= √289
= 17
Therefore, the length of the line segment is 17 units.
To find the length of a side of the dilated polygon, we first need to find the coordinates of the corresponding side in the original polygon. The coordinates of A are (0, -7), and the coordinates of B are (8, 8).
Using the distance formula, we can find the length of AB. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Applying it to our coordinates:
d = √((8 - 0)^2 + (8 - (-7))^2)
= √(8^2 + 15^2)
= √(64 + 225)
= √289
= 17
Therefore, the length of AB is 17.