Question

Pleaseee help me....what will the y-coordinate of b' if ab is dilated by a factor of 2/5, centered at the origin. A=(2,2) B=(10,2)

Answer 1

The y-coordinate of point B' is
`(4)/(5)` or 0.8.

Explanation:

If a figure dilated by scale factor k, centered at the origin, then

`(x,y)\rightarrow(kx,ky)`

It is given that the coordinates of A are (2,2) and coordinates of B are (10,2).

The scale factor is
`(2)/(5)`, so the coordinates of image are

`A(2,2)\rightarrowA'((2)/(5)(2),(2)/(5)(2))\Rightarrow A'((4)/(5),(4)/(5))=A'(0.8,0.8)`

`B(10,2)\rightarrowB'((2)/(5)(10),(2)/(5)(2))\Rightarrow B'(4,(4)/(5))=B'(4,0.8)`

Therefore the y-coordinate of point B' is
`(4)/(5)` or 0.8.

Answer 2

The y-coordinate of B' is equal to 2

Explanation:

step 1

Find the distance of AB

`AB=10-2=8\ units`

step 2

Find the length of A'B'

Multiply the length of AB by the scale factor

`A'B'=8*(2)/(5)= 3.2\ units`

step 3

Find the midpoint AB

`M=((2+10)/(2),(2+2)/(2) )`

`M=(6,2)`

step 4

Find the x-coordinate of B'

The x-coordinate of B' is equal to the x-coordinate of midpoint plus the semi distance A'B'

`6+(3.2)/(2)=6+1.6=7.6`

Find the y-coordinate of B'

The y-coordinate of B' is equal to 2 (because is a horizontal line)