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goblinko [34]
3 years ago
9

Point B is collinear with A and C and partitions AC in a 3:4 ratio. B is located at (4,1) and C is located at (12,5). Find the c

oordinates of endpoint A. Show steps
Mathematics
1 answer:
GrogVix [38]3 years ago
8 0

Answer:

A(-\frac{20}{3} ,-\frac{13}{3})

Step-by-step explanation:

Point B partitions AC in a 3:4 ratio.

B is located at (4,1) and C is located at (12,5).

Let (x_1,y_1) be the coordinates of A.

Then (\frac{mx_1+nx_2}{m+n}, \frac{my_1+ny_2}{m+n})=(4,1)

But m:n=3:4 implies m=3 and n=4 and (x_2=12,y_2=5)

(\frac{3x_1+4*12}{3+4}, \frac{3y_1+4*5}{3+4})=(4,1)

(\frac{3x_1+48}{7}, \frac{3y_1+20}{7})=(4,1)

\frac{3x_1+48}{7}=4, \frac{3y_1+20}{7}=1

3x_1+48=28, 3y_1+20=7

3x_1=-20, 3y_1=-13

x_1=-\frac{20}{3} , y_1=-\frac{13}{3}

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