What are the coordinates of the point on the directed line segment from ( − 8 , − 4 ) (−8,−4) to ( − 5 , 8 ) (−5,8) that partitions the segment into a ratio of 5 to 1?

Answer 1

Trying to find coordinates of point that splits the line between (-8,-4) to (-5,8) at a ratio of 5:1.

Since the ratio is 5:1 we are going find the point that is 5/6 of the distance from (-8,-4) to (-5,8)

The x coordinate of that point will be 5/6 of the distance between -8 and -5 (3) added to -8 = 5/6 * 3 + -8 = -5.5

The y coordinate of that point will be 5/6 of the distance between -4 and 8 (12) added to -4 = 5/6 * 12 + -4 = 6

Coordinate of C is (-5.5,6).

Answer 2

If A(-8 , -4) and B(-5 , 8) are (x1,y1) and (x2,y2) respectively, then

A(-8 ,-4) B(-5 , 8)

(x1,y1) (x2 , y2)

and AC : CB = 5 : 1

a : b

Using the formula ,To find the point C : ( (b x1 + a x2) / (a+b) , (b y1 + a y2) / (a+b) ).

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