Write the system of equations to represent the situation. Use x for the cost of admission and y for the cost of a skate rental. Equation for Receipt 240796:

Equation for Receipt 240797:
240796 has 3 admissions and 2 skate rentals while 240797 had 15 admissions and 10 skate rentals

length of MN is √5 units

length of AC is 2√5 units

Step-by-step explanation:

Here, we want to calculate the coordinates of both midpoints

Mathematically, formula midpoint coordinates are;

(x,y) = (x1 + x2)/2 , (y1 + y2)/2

For AB , coordinates M are as follows

(-5+3)/2,(-4-2)/2 = (-1,-3)

For MN , coordinates of N will be;

(3-1)/2, (-2-6)/2 = (1, -4)

To calculate the distance between two points, we use the formula below;

D = √(x2-x1)^2 + (y2-y1)^2

So for MN ((-1,-3) and (1,-4)

Distance will be

D = √(2^2 + (-1)^2 = √5

For AC, we have

D = √(-4)^2 + (-2)^2 = √20 which is same as 2 √5

MN = √5

AC = 2 √5

Thus;

MN = 1/2 AC