To determine the scale factor used in the dilation of line AB, we can compare the lengths of both lines.
The length of line AB can be found using the distance formula:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((2 - (-3))^2 + (-4 - 4)^2)
= sqrt(5^2 + (-8)^2)
= sqrt(25 + 64)
= sqrt(89)
The length of line A'B' can also be found using the distance formula:
A'B' = sqrt((x2' - x1')^2 + (y2' - y1')^2)
= sqrt((4 - (-6))^2 + (-8 - 8)^2)
= sqrt(10^2 + (-16)^2)
= sqrt(100 + 256)
= sqrt(356)
Therefore, the scale factor is the ratio of the lengths:
scale factor = A'B' / AB
= sqrt(356) / sqrt(89)
≈ 1.89
The scale factor is approximately 1.89.
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 11 to 10 in 1 unit increments and a y axis capped with arrows and ranging from 12 to negative 12 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted. A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 11 to 10 in 1 unit increments and a y axis capped with arrows and ranging from 12 to negative 12 in 1 unit increments. Point upper A is plotted as left parenthesis negative 3 comma 4 right parenthesis and point upper B is plotted as left parenthesis 2 comma negative 4 right parenthesis. The points are joined by a line that extends beyond the points and is capped with arrows at both ends. Point upper A prime is plotted as left parenthesis negative 6 comma 8 right parenthesis and point upper B prime is plotted as left parenthesis 4 comma negative 8 right parenthesis. The points are joined by a line that extends beyond the points and is capped with arrows at both ends.
Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin.
(1 point)
The scale factor is
.
3 answers
no
Apologies for the incorrect answer. Let's try again.
To determine the scale factor, we can compare the corresponding coordinates of points A and A' (both are on the line AB) when taking the center of dilation at the origin.
The coordinates of point A are (-3, 4) and the coordinates of point A' are (-6, 8).
To find the scale factor, we can calculate the ratio of the change in the x-coordinate and the change in the y-coordinate:
Change in x-coordinate: -6 - (-3) = -3
Change in y-coordinate: 8 - 4 = 4
Scale factor = Change in y-coordinate / Change in x-coordinate
= 4 / -3
= -4/3
Therefore, the scale factor is -4/3.
To determine the scale factor, we can compare the corresponding coordinates of points A and A' (both are on the line AB) when taking the center of dilation at the origin.
The coordinates of point A are (-3, 4) and the coordinates of point A' are (-6, 8).
To find the scale factor, we can calculate the ratio of the change in the x-coordinate and the change in the y-coordinate:
Change in x-coordinate: -6 - (-3) = -3
Change in y-coordinate: 8 - 4 = 4
Scale factor = Change in y-coordinate / Change in x-coordinate
= 4 / -3
= -4/3
Therefore, the scale factor is -4/3.
1 answer