Line AB contains point A(−4, 1) and point B (−1, 3). Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.
A′: (−8, 2)
B′: (−2, 6)
To find the coordinates of A' and B' after a dilation with a scale factor of 2 and a center point of dilation at the origin, we can use the dilation formula:
(x', y') = (k * x, k * y)
Where (x, y) represents the original point, (x', y') represents the new point after dilation, and k is the scale factor.
Let's apply this formula to find the coordinates of A' and B':
Coordinates of A':
(x', y') = (2 * x, 2 * y)
= (2 * -4, 2 * 1)
= (-8, 2)
Therefore, A' has the coordinates (-8, 2).
Coordinates of B':
(x', y') = (2 * x, 2 * y)
= (2 * -1, 2 * 3)
= (-2, 6)
Therefore, B' has the coordinates (-2, 6).
So, after the dilation, the coordinates of A' are (-8, 2) and the coordinates of B' are (-2, 6).
To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we can use the formula for dilation.
The formula for dilation with a scale factor of k and a center point of dilation at the origin for a point (x, y) is:
(x', y') = (k * x, k * y)
Let's calculate the coordinates of A' and B' using this formula.
For point A(-4, 1):
x = -4
y = 1
k = 2
Using the formula, we have:
(x', y') = (2 * (-4), 2 * 1) = (-8, 2)
Therefore, the coordinates of A' after dilation are A'(-8, 2).
For point B(-1, 3):
x = -1
y = 3
k = 2
Using the formula, we have:
(x', y') = (2 * (-1), 2 * 3) = (-2, 6)
Therefore, the coordinates of B' after dilation are B'(-2, 6).
In conclusion, the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin are A'(-8, 2) and B'(-2, 6) respectively.