Question

The dashed line triangle is a dilation image of the solid lined triangle

Answer 1

factor of dilation=
`(1)/(3)`

Explanation:

We have been given a diagram in which the dashed line triangle is a dilation image of the solid lined triangle.

Since we know that dilation of a figure changes all the sides of triangle by the same factor.

To find the factor of dilation we will find the length of two corresponding sides of both triangles using distance formula.

`\text{Distance}=√((x_2-x_1)^2+(y_2-y_1)^2)`

Now let us substitute the given coordinates of one side of dashed line triangle.

`\text{Side length of dashed line triangle}=√((-2-2)^2+(0--2)^2)`

`\text{Side length of dashed line triangle}=√((-4)^2+(2)^2)`

`\text{Side length of dashed line triangle}=√(16+4)`

`\text{Side length of dashed line triangle}=√(20)`

`\text{Side length of dashed line triangle}=2√(5)`

Now let us find the length of corresponding side of solid lined triangle.

`\text{Side length of solid lined triangle}=√((-6-6)^2+(0--6)^2)`

`\text{Side length of solid lined triangle}=√((-12)^2+(6)^2)`

`\text{Side length of solid lined triangle}=√(144+36)`

`\text{Side length of solid lined triangle}=√(180)`

`\text{Side length of solid lined triangle}=6√(5)`

Upon comparing side lengths of both triangles we will get,

`\frac{\text{Dashed line length}}{\text{Solid line length}}= (2√(5))/(6√(5))`

`{\text{Dashed line length}}= (1)/(3)*{\text{Solid line length}`

We can see that the length of dashed line is 1/3 the length of solid line, therefore, the factor of dilation is 1/3.