Question

20 POINTS!!!!! A cartographer is making a city map. Line m represents Murphy Street. The cartographer translates points on line m along the vector angleleft1, −3angleright to draw Nolan Street. Draw the line for Nolan Street on the coordinate plane and complete its equation. What is the image of (0, 3) in this situation?

Answer 1

`y=2x-2` and image of (0,3) is (1,0).

Explanation:

From the given graph it is clear that the line of Nolan Street passes through the points (0,-2) and (1,0).

So, the equation of Nolan Street is

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

`y-(-2)=(0-(-2))/(1-0)(x-0)`

`y+2=2x`

`y=2x-2`

So, the equation of the Nolan Street is
`y=2x-2`.

It is given that the cartographer translates points on line m along the vector <1, −3> to draw Nolan Street. So, the rule of translation is

`(x,y)\to (x+1,y-3)`

The image of (0, 3) in this situation.

`(0,3)\to (0+1,3-3)=(1,0)`

The image of (0,3) is (1,0).