segment PQ with endpoints P(4,2) and Q(2,17) is dilated by a scale factor of 4. Find the length of segment P',Q'
PQ has length √(2^2+15^2) = √229
P'Q' has length 4 times that.
To find the length of segment P'Q', we first need to find the coordinates of P' and Q' after the dilation.
Given that the segment PQ is dilated by a scale factor of 4, we can find the coordinates of P' and Q' using the following formula:
P' = (4 * x-coordinate of P, 4 * y-coordinate of P)
Q' = (4 * x-coordinate of Q, 4 * y-coordinate of Q)
Using this formula, let's calculate the coordinates of P' and Q':
For P':
x-coordinate of P' = 4 * x-coordinate of P = 4 * 4 = 16
y-coordinate of P' = 4 * y-coordinate of P = 4 * 2 = 8
So, P' = (16, 8)
For Q':
x-coordinate of Q' = 4 * x-coordinate of Q = 4 * 2 = 8
y-coordinate of Q' = 4 * y-coordinate of Q = 4 * 17 = 68
So, Q' = (8, 68)
Now that we have the coordinates of P' and Q', we can find the length of segment P'Q' using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, let's calculate the length of segment P'Q':
Length of P'Q' = √((x-coordinate of Q' - x-coordinate of P')^2 + (y-coordinate of Q' - y-coordinate of P')^2)
= √((8 - 16)^2 + (68 - 8)^2)
= √((-8)^2 + (60)^2)
= √(64 + 3600)
= √3664
≈ 60.53
Therefore, the length of segment P'Q' is approximately 60.53.