First, find the side length: |KL|=sqrt((1-4)^2+(3-(-4))^2)

=sqrt(58).

Denote coordinates of N by (x,y).

The length |NK| equals sqrt(58), i.e. (x-1)^2+(y-3)^2=58.

The slope of NK is the same as the slope of ML,

i.e. (x-1)/(y-3)=(-3-4)/(-7-(-4))

=7/3.

Solving these simultaneous equations we find two solution:

x=-6, y=0 and x=8, y=6

The correct solution is the first one, as it satisfies |NM|=sqrt(58)

We need the distance from L to K to equal the distance from M to N. Fill in the numbers you know.

L to K on the x-axis is 4 minus 1 = 3.

L to K on the yaxis is -4 minus 3 = -7

Now M to N must be the same distances. So we plug in the distances just determined and the point info we already know:

M to N on the x axis is the number of M on the x-axis (-3)minus the unknown number which equals 3 (distance L to K on x-axis above)

M to N on the x-axis is -3 minus x = 3, x=-6

M to N on the Y-axis is the number of M on the y-axis (-7) minus the unknown ‘y’ equals the distance from L to K determined above (-7):

M to N on the y axis is -7 minus y = -7, x = 0

So the points are (-6, 0) for N.