lilrahman
Answered

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In quadrilateral ABCD, ∠ABC is a right angle and AB = 4 units. Quadrilateral ABCD is dilated by a scale factor of 2 with point B as the center of dilation, resulting in the image, quadrilateral A'B'C'D'. Which statement is true?
A.
A'B' is 8 units long and lies on the same line as AB.
B.
A'B' is 6 units long but lies on a different line than AB.
C.
A'B' is 8 units long but lies on a different line than AB.
D.
A'B' is 6 units long and lies on the same line as AB.

Sagot :

reinhard10158

Answer:

A

Step-by-step explanation:

the scale factor applies to all lines and dimensions. so, the new, dilated line will be the length of the original line × 2.

that means 8 units.

and since B is the center, the original line AB will be mirrored and stretched to the other side of B (meaning B' = B). therefore, AB and A'B' are then on on line (with the length of 4+8 = 12 units).

A'B' is 8 units long and lies on the same line as AB. so option A is correct.

How dilation of a quadrilateral works?

Dilation of a figure will leave its sides get scaled (multiplied) by same number.

Dilation if, is from the center of the quadrilateral, then the distance of all the points of the quadrilateral from its center will get scaled by that dilation factor.

In quadrilateral ABCD, ∠ABC is a right angle, and AB = 4 units.

Quadrilateral ABCD is dilated by a scale factor of 2 with point B as the center of dilation, resulting in the image, quadrilateral A'B'C'D'.

The scale factor applies to all lines and dimensions.

so, the new, dilated line will be twice the length of the original line.

that means 8 units.

Since B is the center, the original line AB will be mirrored and stretched to the other side of B (meaning B' = B).

AB and A'B' are then online (with the length of 4+8 = 12 units).

Hence, A'B' is 8 units long and lies on the same line as AB. so option A is correct.

Learn more about dilation;

https://brainly.com/question/2514486

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