Question

What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE

Answer 1

Given:

The equation of a line is:

`2y+3x=10`

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

`2y+3x=10`

For
`x=0`,

`2y+3(0)=10`

`2y+0=10`

`y=(10)/(2)`

`y=5`

For
`x=2`,

`2y+3(2)=10`

`2y+6=10`

`2y=10-6`

`2y=4`

Divide both sides by 2.

`y=(4)/(2)`

`y=2`

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

`(x,y)\to (3x,3y)`

Using this rule, we get

`A(0,5)\to A'(3(0),3(5))`

`A(0,5)\to A'(0,15)`

Similarly,

`B(2,2)\to B'(3(2),3(2))`

`B(2,2)\to B'(6,6)`

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-15=(6-15)/(6-0)(x-0)`

`y-15=(-9)/(6)(x)`

`y-15=(-3)/(2)x`

Multiply both sides by 2.

`2(y-15)=-3x`

`2y-30=-3x`

`2y+3x=30`

Therefore, the equation of the line after the dilation is
`2y+3x=30`.