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Math  /  Geometry

QuestionDilate △FGH\triangle F G H by a scale factor of 4 with the center of dilation at the origin.
How can you use the coordinates of point FF to find the coordinates of point F′F^{\prime} ?
Add 4 to each coordinate.
Subtract 4 from each coordinate.
Multiply each coordinate by 4.
Divide each coordinate by 4.

Studdy Solution

STEP 1

1. The center of dilation is at the origin (0,0)(0, 0).
2. The scale factor for dilation is 44.
3. We are finding the coordinates of the dilated point F′F' from the original point FF.

STEP 2

1. Recall the rule for dilation with respect to the origin.
2. Apply the dilation rule to the coordinates of point FF.

STEP 3

Recall the rule for dilation with respect to the origin:
When a point (x,y)(x, y) is dilated by a scale factor kk with the center of dilation at the origin, the coordinates of the image (x′,y′)(x', y') are given by:
x′=k⋅x x' = k \cdot x y′=k⋅y y' = k \cdot y

STEP 4

Apply the dilation rule to the coordinates of point FF:
Given the scale factor k=4k = 4, if the original coordinates of point FF are (x,y)(x, y), the coordinates of the dilated point F′F' will be:
x′=4⋅x x' = 4 \cdot x y′=4⋅y y' = 4 \cdot y
Therefore, to find the coordinates of point F′F', multiply each coordinate of point FF by 44.
The correct operation is to multiply each coordinate by 4.

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