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Natali [406]
3 years ago
5

Find the coordinates of the point 7/10 of the way from A to B. A(-4,-7) B(12,4)

Mathematics
1 answer:
krok68 [10]3 years ago
7 0

Answer:

C(7.2,0.7)

Step-by-step explanation:

Let point C be \frac{7}{10} of the way from A to B, then AC:CB=7:3.

If point C(x_C,y_C) divides segment AB with endpoints A(x_A,y_A),\ B(x_B,y_B) in the ratio m:n, then

x_C=\dfrac{nx_A+mx_B}{m+n}\\ \\y_C=\dfrac{ny_A+my_B}{m+n}

In your case, A(-4,-7) and B(12,4), so

x_C=\dfrac{3\cdot (-4)+7\cdot 12}{7+3}=\dfrac{-12+84}{10}=7.2\\ \\y_C=\dfrac{3\cdot (-7)+7\cdot 4}{7+3}=\dfrac{-21+28}{10}=0.7

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