Original content copyright © by houghton mifflin harcourt. additions and changes to the original content are the responsibility of the instructor. distance and midpoint formulas segment with endpoints at (−4, 10) and (−6, −2) 4. segment with endpoints at (−1, 15) and (3, 0) 5. segment with endpoints at (2, −3) and (−2, −5)

a) D = √148

                 m = (-5,4)

b) D = √241

m = (1, 7.5)

c) D = √20

m = (0,-4)

Step-by-step explanation:

Distance and Midpoint Formulas

distance = D = √[(x₂-x₁)² + (y₂-y₁)²]

Midpoint: m = ((x₂+x₁)/2 , (y₂+y₁)/2)

(−4, 10) and (−6, −2)

D = √[(-6-(-4))² + (-2-10)²] = √[(-6+4))² + (-2-10)²] = √[(-2))² + (-12)²] =

√[4 + 144] = √148

m = ((-6+(-4))/2 ; (-2+10)/2

m = (-10/2 ; 8/2)

m = (-5,4)

(−1, 15) and (3, 0)

D = √[(3-(-1))² + (0-15)²] = √[(3+1))² + (0-15)²] = √[(4)² + (-15)²] =

√[16 + 225] = √241

m = ((3+(-1))/2 ; (0+15)/2

m = (2/2 ; 15/2)

m = (1,7.5)

(2, −3) and (−2, −5)

D = √[(-2-2)² + ((-5)-(-3)²] = √[(-4))² + (-5+3)²] = √[(-4)² + (-2)²] =

√[16 + 4] = √20

m = (-2+2))/2 ; (-5+(-3))/2

m = (0/2 ; -8/2)

m = (0,-4)

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square