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Fynjy0 [20]
3 years ago
5

Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segmen

t in the ratio of 5:2. A. (-5, -15) B. (-23, -5) C. (-13, -7) D. (-11.5, -2.5)
Mathematics
1 answer:
Nataly_w [17]3 years ago
6 0

Answer:

C. (-13, -7)

Step-by-step explanation:

The location of a point O(x, y) that divides a line AB with location A(x_1,y_1) and B(x_2,y_2) in the ratio m:n is given by:

x=\frac{m}{m+n} (x_2-x_1)+x_1\\\\y=\frac{m}{m+n} (y_2-y_1)+y_1

Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:

x=\frac{5}{5+2} (-15-(-8))+(-8)\\\\x=\frac{5}{7} (-15+8)-8=\frac{5}{7}(-7)-8=-5-8=-13 \\\\\\y=\frac{5}{5+2} (-13-8)+8\\\\y=\frac{5}{7} (-21)+8=5(-3)+8=-15+8=-7

Therefore the coordinates of point X is at (-13, -7)

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