Question

I don’t understand how to find out if lines are parallel

Answer 1

2, 4, -2,-2

1) Examining the graph, let's write down the coordinates of each of those points:

M(-2,0) M' (6,-4)

N (-6,8) N' (2,4)

2) Picking the points as a reference, we can answer those questions. We can see that the line MN was translated 2 units down (Note the position from M and M').

And MN was also translated to the right 4 units.

3) We are going to need to make use of the slope formula to get the slope of MN:

`m_(MN)=(y_2-y_1)/(x_2-x_1)=(8-0)/(-6-(-2))=(8)/(-6+2)=(8)/(-4)=-2`

Note that we are considering the coordinates of M and N for this calculation.

And likewise, for the M'N' (the transformed line) we've got:

`m_(M^(\prime)N^(\prime))=(4-(-4))/(2-6)=(8)/(-4)=-2`

Notice that since the slope of MN and M'N' are the same, then we can verify that these are parallel lines.

4) Thus the answers are:

`\begin{gathered} a)2 \\ b)4 \\ -2 \\ -2 \end{gathered}`