Question

Question 1 - A point M on a segment with endpoints X (1,-2) and Y (10,3) partitions the segment in a 5:1 ratio Find M

Answer 1

The value of M based on the information about the segment is

How to find the value?

Since segment XY is divided in the ratio 5:1, it is divided into 6 equal sections. (6 = 5+1). 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 5/6 of the way from X to Y.

• x-coordinate of M = 1 + (5/6)(9) = 1 + 7.5 = 8.5
• y-coordinate of M = -2 + (5/6)(5) = -2 + 4 1/6 = 2 1/6

Therefore, M = (8 1/2, 2 1/6).

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