Question

A point M on a segment with endpoints X(1, −2) and Y(10, 3) partitions the segment in a 4:1 ratio. Find M. You must show all work to receive credit. (10 points)

Answer 1

Answer:

(8.2,2)

Step-by-step explanation:

1.

4:1 ratio means XY divided into 5 equal sections. (5 = 4+1)

4:1 ratio means (4/(4+1))

4:1 ratio means (4/5)

2.

4:1 ratio means M is 4/5 of the way from the initial point X(1, −2)

3.

get the x and y distances between (1, −2) and  (10, 3)

x2-x1=9

y2-y1=5

4.

since  initial point is (1, −2)

you add 1 to the new x value and

you add -2 to the new y value

ANSWERS:

x-coordinate of M = 1 + (4/5)(9) = 1 + 7.2 = 8.2

y-coordinate of M = -2 + (4/5)(5) = -2 + 4 = 2

As we move along XY from X to Y,

x increases by 9 and

y increases by 5

M is the point on XY that is 4/5 of the way from X to Y.

M is 4/5 of the distance from (1,-2) to (10,3).

To find M x and y coordinates 4/5 of distance between (x1,y1) and (x2,y2):

To find M x and y coordinates 4/5 of distance between (1,-2) and (10,3):

x-coordinate of M = 1 + (4/5)(9) = 1 + 7.2 = 8.2

y-coordinate of M = -2 + (4/5)(5) = -2 + 4 = 2

wyzant

jon s.

mark m.

Raymond B.