To find the scale factor used in the dilation of line segment AB, we can compare the lengths of AB and A' B'.
The coordinates of A are (2, 3) and B are (4, 1). The length AB is the distance between these two points.
AB = √((x₂ - x₁)² + (y₂ - y₁)²)
AB = √((4 - 2)² + (1 - 3)²)
AB = √(2² + (-2)²)
AB = √(4 + 4)
AB = √8
AB = 2√2
The coordinates of A' are (6, 9) and B' are (12, 3). The length A' B' is the distance between these two points.
A' B' = √((x₂ - x₁)² + (y₂ - y₁)²)
A' B' = √((12 - 6)² + (3 - 9)²)
A' B' = √(6² + (-6)²)
A' B' = √(36 + 36)
A' B' = √72
A' B' = √(36 * 2)
A' B' = 6√2
The scale factor can be found by dividing the length of A' B' by the length of AB.
Scale factor = A' B' / AB
Scale factor = (6√2) / (2√2)
Scale factor = 6/2
Scale factor = 3
Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 3.
Use the image to answer the question.
A coordinate plane with four quadrants shows x-axis ranging from negative 5 to 12 in increments of 1 and the y-axis from 17 to negative 4 in increments of 1. Points upper A, upper B, upper A prime, and upper B prime are plotted on quadrant 1. The plotted points are as follows: Upper A is left parenthesis 2 comma 3 right parenthesis and upper B is left parenthesis 4 comma 1 right parenthesis. The points are joined by a line. Upper A prime is plotted as left parenthesis 6 comma 9 right parenthesis and upper B prime as left parenthesis 12 comma 3 right parenthesis. The points are joined by a line.
Determine the scale factor used in the dilation of line segment AB, centered at the origin.
(1 point)
The scale factor is
.
1 answer