Question

Polygon ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to create polygon A′B′C′D′. If the endpoints of line AB are located at (0, -7) and (8, 8), what is the length of line A'B'?

Use the distance formula to help you decide (picture added)

Answer 1

A'B' = 34 units

Explanation:

Since the dilatation is centred at the origin , then multiply the coordinates by 2

A' = (2(0), 2(- 7) = (0, - 14 )

B' = (2(8), 2(8) = (16, 16)

Calculate the length using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = A'(0, - 14) and (x₂, y₂ ) = B'(16, 16)

d =
`√((16-0)^2+(16+14)^2)`

=
`√(16^2+30^2)`

=
`√(256+900)`

=
`√(1156)`

= 34