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.

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).

b

step-by-step explanation:

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)