Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 4, centered at the origin where the endpoints are A(−2,−3) and B (−4,−5).(1 point)
A′(−8,−12) and B′ (−16,−20)
To find the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 4, centered at the origin, you need to multiply the coordinates of each point by the scale factor.
Let's start with point A(−2,−3):
1. Multiply the x-coordinate by the scale factor: -2 * 4 = -8.
2. Multiply the y-coordinate by the scale factor: -3 * 4 = -12.
So, the coordinates of point A′ after dilation are (-8, -12).
Now, let's do the same for point B(−4,−5):
1. Multiply the x-coordinate by the scale factor: -4 * 4 = -16.
2. Multiply the y-coordinate by the scale factor: -5 * 4 = -20.
Therefore, the coordinates of point B′ after dilation are (-16, -20).
So, the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 4, centered at the origin, are A′(-8, -12) and B′(-16, -20) respectively.
To perform a dilation of the line segment AB with a scale factor of 4, centered at the origin, we can multiply each coordinate of A and B by the scale factor.
Let's find the coordinates of A':
A' = (scale factor * x-coordinate of A, scale factor * y-coordinate of A)
= (4 * -2, 4 * -3)
= (-8, -12)
And now for B':
B' = (scale factor * x-coordinate of B, scale factor * y-coordinate of B)
= (4 * -4, 4 * -5)
= (-16, -20)
Therefore, A' is (-8, -12) and B' is (-16, -20) after the dilation.