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

Answer:

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

Step-by-step 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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-(-2)=\dfrac{0-(-2)}{1-0}(x-0)$

$y+2=2x$

$y=2x-2$

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).