Question

Is quadrilateral jklm the result of a dilation of quadrilateral abcd by a scale factor of 2? why or why not?

Answer: No,Because sides JM and KL have different slopes from sides AD and BC

Answer 1

No. Because sides JM and KL have different slopes from sides AD and BC .

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

For AD:

We have the points A(2, -2) and D(1, -4). Substitute:

`m=(-4-(-2))/(1-2)=(-2)/(-1)=2`

For JM:

We have the points J(4, -4) and M(2, -9). Substitute:

`m=(-9-(-4))/(2-4)=(-5)/(-2)=2.5`

`2\\eq2.5`

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Another argument.

No. Because the MJ is not twice as long as AD.

The formula of the length of a segment:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

The length of AD:

`|AD|=√((1-2)^2+(-4-(-2))^2)=√((-1)^2+(-2)^2)=√(1+4)=\sqrt5`

The length of MJ:

`|MJ|=√((2-4)^2+(-9-(-4))^2)=√((-2)^2+(-5)^2)=√(4+25)=√(29)`

`√(29)\\eq2\sqrt5`