the coordinates of the endpoints of CE are C(-3, -7) and E(7, -2). point M (3, -4) is on CE

Question

the coordinates of the endpoints of CE are C(-3, -7) and E(7, -2). point M (3, -4) is on CE

Answer 1

distance MC = sqrt ( (3 - -3)^2 + (-4 - -7)^2 )

= sqrt ( 6^2 + 3^2)

= sqrt ( 36 + 9)

= sqrt(45)

= 3 * sqrt(5)

distance ME = sqrt ( (7-3)^2 + (-4 - -2)^2)

= sqrt ( 4^2 + (-2)^2))

= sqrt( 16+ 4)

= sqrt(20)

= 2 * sqrt(5)

MC + ME = 5 * sqrt(5)

CE = sqrt ( (-3 - 7)^2 + (-7 + -2)^2)

= sqrt ( (-10)62 + (-5)^2)

= sqrt ( 100 + 25)

= sqrt(125)

= 5 * sqrt(5)

Answer 2

the coordinates of the endpoints of CE are C(-3, -7) and E(7, -2). point M (3, -4) is on CE. What is the ratio of CM:ME? This is a distance formula problem, where you are comparing the two ratio's of CM to ME.

It is well worth your time to memorize the distance formula: d = sqrt ((x - x₁)² + (y - y₁)²) using two points: (x,y), (x₁,y₁). You will use this many, many times in your math classes.

1. CM: sqrt ((-3 - 3)² + (-7 - -4)²) = sqrt ((6)² + (-3)²) = sqrt (45) ≅ 6.71
2. ME: sqrt ((3 - 7)² + (-4 - -2)²) = sqrt ((-4)² + (-2)²) = sqrt (20) ≅ 4.47
3. CM:ME (6.71:4.47) = 1.5 : 1