<span>Rectangle with vertexes of (4,4), (-4,4), (4,10), and (-4,10)
I can't do your graph for you, but I can help with the coordinates of the final polygon. In general to scale (x,y) by s centered at (a,b) that would mean that (x,y) maps to ((x-a)*s+a, (y-b)*s+b). And since we've been given (a,b) = (0,0), the mapping simplifies to (x,y) maps to (x*s, y*s). So let's do it:
Point (2,2) ==> (2*2,2*2) = (4,4)
Point (-2,2) ==> (-2*2,2*2) = (-4,4)
Point (2,5) ==> (2*2,5*2) = (4,10)
Point (-2,5) ==> (-2*2,5*2) = (-4,10)
So your desired polygon is a rectangle with vertexes of (4,4), (-4,4), (4,10), and (-4,10)</span>
Your scaling in the x direction is OK, but you didn't scale in the y direction properly. Hint. Scale each vertex of the original rectangle independently to construct the scaled rectangle. I see the original points and their scaling by 2 as (2,2) - Scales to (2*2, 2*2) = (4,4) OK in your drawing. (-2,2) - Scales to (-2*2, 2*2) = (-4,4) OK in your drawing. (2,5) - Scales to (2*2, 5*2) = (4,10) Error in your drawing. (-2,5) - Scales to (-2*2, 5*2) = (-4,10) Error in your drawing.
This is a system of equations. We solve it by setting it up so that when we add the two equations together, one of the variables will cancel out. We can do this by multiplying the bottom equation by 3. This will make our system of equations equal:
3a + b + 225 -3a + 3b = 75
Now we add these two equations together, because the a terms will cancel out.
4b = 300.
We can find what b is by dividing both sides by 4.
b = 75
Next, we plug in b in one of the equations and solve for a. You can use either equation, but I will use the second.
75 - a = 25
Subtract 25 from both sides and add a to both sides:
a = 50
So, the first option is correct. A = 50 and b = 75.
