Triangle PQR has vertices P(0, 0), Q(3, 4), and R(3, 0). If triangle PQR is rotated 180° about the origin, what is the length of side P'R?
To find the length of side P'R, we first need to find the coordinates of point R' after the rotation.
To rotate a point (x, y) 180° about the origin, we need to multiply the coordinates by -1.
Coordinates of R' after rotation = (-3, 0)
To find the length of side P'R, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For points P(0, 0) and R'(-3, 0), the distance formula becomes:
Distance = √((-3 - 0)^2 + (0 - 0)^2)
= √((-3)^2 + 0^2)
= √(9)
= 3
Therefore, the length of side P'R is 3 units.
To find the length of side P'R after rotating triangle PQR 180° about the origin, we need to determine the new coordinates of point R' after the rotation.
To rotate a point (x, y) 180° about the origin, we can use the following formulas:
x' = -x
y' = -y
Let's apply these formulas to the coordinates of point R (3, 0):
x' = -3
y' = -0 = 0
Therefore, the new coordinates of point R' after rotating 180° about the origin are R'(-3, 0).
Now, we can find the length of side P'R using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In our case, P'(0, 0) and R'(-3, 0). Plugging these values into the distance formula, we have:
d = √((-3 - 0)^2 + (0 - 0)^2)
= √(9 + 0)
= √9
= 3
Therefore, the length of side P'R is 3.