Question

Triangle STV was dilated with the origin as the center of dilation to form Triangle S'T'V'. On a coordinate plane, triangles S T V and S prime T prime V prime are shown. Triangle S T V has points (0, 6), (negative 3, negative 6), and (3, negative 6). Triangle S prime T prime V prime has points (0, 2), (negative 1, negative 2) and (1, negative 2). What is the scale factor of the dilation?

Answer 1

Answer:   1/3

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Explanation:

Triangle STV has points at locations

S = (0, 6)

T = (-3, -6)

V = (3, -6)

Triangle S'T'V' has points at locations

S ' = (0, 2)

T ' = (-1, -2)

V ' = (1, -2)

Pick on just one pair of corresponding points. I'll pick on points S and S'

Going from S = (0,6) to S ' = (0, 2), note how the y coordinate has been divided by 3. This is the same as multiplying by 1/3. Therefore, the scale factor is 1/3

We can see this happening with points T and T ' as well

T = (-3, -6) to T ' = (-1, -2) also has each coordinate multiplied by 1/3

The same can be said from V to V' also.

Because the scale factor is 1/3, this means that the side lengths of the image triangle S'T'V' are 1/3 as long as the preimage triangle STV.

Answer 2

The scale factor of the dilation is $\dfrac{1}{3}$.

It is given that,

• STV is dilated to S'T'V'.
• Triangle STV has points $(0, 6), (-3,-6)$ and $(3,-6)$.
• Triangle S'T'V' has points $(0, 2), (-1,-2)$ and $(1,-2)$.

Explanation:

If a figure is dilated with the origin as the center of dilation. Then, the rule of dilation is defined as:

$(x,y)\to (kx,ky)$

Where, $k$ is the scale factor.

Using this rule, we get

$(0,6)\to (0,6k)$

The image of (0,6) is (0,2). So,

$(0,6k)=(0,2)$

$6k=2$

$k=\dfrac{2}{6}$

$k=\dfrac{1}{3}$

Thus, the scale factor of the dilation is $\dfrac{1}{3}$.

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