Question

Triangle LMN with vertices L(0, 3), M(3, 4), and N(1, 2): a) 180° rotation about the origin b) dilation with scale factor of 2 using the origin as the center

Answer 1

`L`
`M`
`N`

Explanation:

Given

`L = (0,3)`

`M = (3,4)`

`N = (1,2)`

Required

Determine the new coordinates of L, M and N

Applying (a): 180 degrees rotation about the origin

When
`(x,y)` is rotated about 180 degrees, the new point becomes
`(-y,-x)`

So:

`L = (0,3)` ==>
`L' = (-3,0)`

`M = (3,4)` ==>
`M' = (-4,-3)`

`N = (1,2)` ==>
`N' = (-2,-1)`

Applying (b): Dilation of scale factor, 2

The formula to apply here is;

`New = Old * Scale\ Factor`

So:

`L' = (-3,0)` becomes:

`L`

`L`

`L`

`M' = (-4,-3)` becomes:

`M`

`M`

`M`

`N' = (-2,-1)`

`N`

`N`

`N`

Hence;

The new coordinates are:

`L`

`M`

`N`