Question

Square RSTU dilates by a factor of ½ with respect to the origin to create square R'STU'. If R'S' is 2 units, what is Rs?

a) 2 units
b) 0.5 units
c) 4 units
d) 1 unit

Answer 1

Square RSTU is dilated by a factor of 1/2 to create Square R'S'T'U'. Given that R'S' is 2 units, to find RS in the original square, we multiply 2 units by the inverse dilation factor, resulting in RS being 4 units.

Step-by-step explanation:

The student has asked about a dilation of Square RSTU by a factor of ½ with respect to the origin to create Square R'S'T'U'. Given that side R'S' is 2 units in the dilated square, we aim to find the length of the side RS in the original square.

Since the dilation factor is ½, the original square is dilated to half its size. Therefore, each side of the original square must be twice the length of its corresponding side in the dilated square. If R'S' = 2 units, to find RS, we simply need to multiply this by the inverse of the dilation factor, which is 2 (since 1/½ = 2).

RS = R'S' × 2 = 2 units × 2 = 4 units.