Find the length of the line segment joining each pair of points.(Show as exact solution) a) M(3,7) and A(1,3) b) B(5,-1) and C(-3,4)?

Length of line segment joining (x₁, y₁) and (x₂, y₂) = √[(x₁ - x₂)² + (y₁ - y₂)²]

a)
Length of the line segment = √[(3 - 1)² + (7 - 3)²] = √[4 + 16] = √20 = 2√5

b)
Length of the line segment = √[(5 - (-3))² + (-1 - 4)²] = √[64 + 25] = √89

M(3,7) & A(1,3)

First find the rise (change in y) and run (change in x)

Change in y = 7 - 3 = 4
Change in x = 3 - 1 = 2

Now apply Pythagoras:

c² = a² + b²
c² = 4² + 2²
c² = 16 + 4
c² = 20
c = √20
c = 2√5 <-- length of line connecting M & A

You can do the second.

Plug into the distance formula (which is just the Pythagorean theorem adapted to coordinate geometry).

a) √( (3-1)² + (7-3)² ) = √( 2² + 4² ) = √( 4+16 ) = √20 = 2√5
b) similar

Use a calculator