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kramer
3 years ago
6

Segment CD has endpoints (-4, 3) and (8, -1). Find the coordinates of the point that divides the line segment directed from C to

D in the ratio of 2:3. A) ( -6 5 , 26 5 ) B) ( -4 5 , 7 5 ) C) ( 1 5 , 13 5 ) D) ( 16 5 , 3 5 )
Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
3 0

Answer:

A(0.8,\ 1.4)\ \text{or }\ A\left(\dfrac{4}{5},\dfrac{7}{5}\right)

Step-by-step explanation:

If point A(x,y) divides the segment with endpoints  C(x_1,y_1) and D(x_2,y_2) in the ratio m:n,

then

x=\dfrac{nx_1+mx_2}{m+n}\\ \\y=\dfrac{ny_1+my_2}{m+n}

In your case,

C(-4,3)\\ \\D(8,-1)\\ \\m:n=2:3

then

x=\dfrac{3\cdot (-4)+2\cdot 8}{2+3}=\dfrac{-12+16}{5}=\dfrac{4}{5}=0.8\\ \\y=\dfrac{3\cdot 3+2\cdot (-1)}{2+3}=\dfrac{9-2}{5}=\dfrac{7}{5}=1.4

Thus,

A(0.8,\ 1.4)\ \text{or }\ A\left(\dfrac{4}{5},\dfrac{7}{5}\right)

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