Note: enter your answer and show all the steps that you used to solve this problem in the space provided the endpoints of AB are A(9, 4) and B(5, -4). the endpoints of its image are A'(6, 3) and B'(3, -3). find the scale factor and explain each of your steps
To find the scale factor, we can use the formula:
Scale factor = (length of the image) / (length of the original)
First, let's calculate the lengths of both the original and the image:
Original length AB = sqrt((x₂ - x₁)² + (y₂ - y₁)²)
= sqrt((5 - 9)² + (-4 - 4)²)
= sqrt((-4)² + (-8)²)
= sqrt(16 + 64)
= sqrt(80)
= 4√5
Image length A'B' = sqrt((x₂' - x₁')² + (y₂' - y₁')²)
= sqrt((3 - 6)² + (-3 - 3)²)
= sqrt((-3)² + (-6)²)
= sqrt(9 + 36)
= sqrt(45)
= 3√5
Now we can find the scale factor:
Scale factor = (length of the image) / (length of the original)
= (3√5) / (4√5)
= 3/4
Therefore, the scale factor is 3/4.
Explanation of steps:
1. Use the distance formula to find the lengths of AB and A'B'.
2. Plug in the coordinates of the endpoints to the distance formula.
3. Simplify the expressions inside the square root and calculate the values.
4. Use the formula to calculate the scale factor.