Square A is dilated by a scale factor of 1/2 making a new square F (not shown). Which square above would have the same area as square F?
a
Square B
b
Square C
c
Square D
d
Square E
Square B
To determine which square above would have the same area as the new square F, we need to understand how the scale factor affects the area.
Dilating a shape by a scale factor of 1/2 means that all the sides of the new shape will be half the length of the original shape. Since square A is dilated to create square F, the side length of square F is half the side length of square A.
To find the area of a square, we square the length of one of its sides.
Given that the new square F is half the size of square A, its side length would be (1/2) * the side length of square A. Therefore, the area of the new square F would be [(1/2) * side length of square A]^2.
To compare this with the areas of the squares above (B, C, D, and E), we need to investigate their side lengths:
a) Square B: No information is given about its side length.
b) Square C: No information is given about its side length.
c) Square D: No information is given about its side length.
d) Square E: No information is given about its side length.
Since we don't have any information about the side lengths of squares B, C, D, and E, we cannot determine which square would have the same area as square F without additional information.