When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation w

Question

Wittaler

2 months ago

7

When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation w

as a dilation. Generate instructions you would give another student to determine the scale factor.

Mathematics

2 answers:

Inessa [12.5K] · Answer 1 · 2026-03-24T07:04:49+03:00

Let’s assume the initial coordinates are (x,y) while the dilated coordinates are (x',y').

Thus, the dilation process can be represented as:
(x,y)............> (x',y')

Now, let’s say the dilation factor is k.
Hence:
x' = kx
y' = ky

Using this information, the student simply needs to take the initial coordinates and final coordinates and substitute them into either of the equations above to solve for k.

Example:
Assuming an original point of (2,4) expands to (4,8). Determine the dilation factor.
Let k represent the dilation coefficient.
The coordinates (x,y) are (2,4) and (x',y') are (4,8)
Thus:
x' = kx.........> 4 = k*2..........> k = 2
Alternatively:
y' = ky..........> 8 = k*4.........> k = 2
Consequently, the dilation coefficient is 2.

Hopefully, this is helpful:)

Svet_ta [12.7K] · Answer 2 · 2026-03-24T07:05:49+03:00

Sample Response: Identify two corresponding ordered pairs from the two shapes. Determine how much the pre-image values were multiplied to achieve the image values, as this represents your scale factor. You can obtain this by dividing the coordinates of the image by the matching coordinates of the pre-image.