A rectangle has vertices -5,6 -1,6 -1,3 -5,3 and . It is first dilated by the rule and then translated 10 units down. What are the coordinates of the image?
To find the coordinates of the image, we first need to dilate the rectangle by the rule and then translate it 10 units down.
Dilation by the rule means multiplying each coordinate by the given factor. Let's say the dilation factor is k.
The original coordinates of the rectangle are:
A(-5, 6), B(-1, 6), C(-1, 3), D(-5, 3)
Let's say the dilation factor is 2. Then the coordinates of the dilated rectangle would be:
A'(-5*2, 6*2) = A'(-10, 12)
B'(-1*2, 6*2) = B'(-2, 12)
C'(-1*2, 3*2) = C'(-2, 6)
D'(-5*2, 3*2) = D'(-10, 6)
Now we need to translate the coordinates 10 units down:
A"(-10, 12 - 10) = A'(-10, 2)
B'(-2, 12 - 10) = B'(-2, 2)
C'(-2, 6 - 10) = C'(-2, -4)
D'(-10, 6 - 10) = D'(-10, -4)
So, the coordinates of the image after dilating by a factor of 2 and then translating 10 units down are:
A'(-10, 2), B'(-2, 2), C'(-2, -4), D'(-10, -4)