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navik [9.2K]
3 years ago
6

Suppose line segment AB has one endpoint at A(0, 0). What are the coordinates of B if (5, 3) is 1/3 of the way from A to B?

Mathematics
1 answer:
prisoha [69]3 years ago
5 0

Answer:

B(x_2,y_2)= (20,12)

Step-by-step explanation:

Given

A = (0,0)

Ratio; m : n = 1 : 3

Point\ at\ 1 : 3 = (5,3)

Required

Coordinates of B

This question will be answered using line ratio formula;

(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})

In this case:

(x,y) = (5,3)

(x_1,y_1) = (0,0)

m : n = 1 : 3

Solving for (x_2,y_2)

(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n}) becomes

(5,3) =  (\frac{1 * x_2 + 3 * 0}{1 + 3},\frac{1 * y_2 + 3 * 0}{1 + 3})

(5,3) =  (\frac{x_2 + 0}{4},\frac{y_2 + 0}{4})

(5,3) =  (\frac{x_2}{4},\frac{y_2}{4})

Comparing the right hand side to the left;

\frac{x_2}{4} = 5 -- (1)

\frac{y_2}{4} = 3 -- (2)

Solving (1)

x_2 = 5 * 4

x_2 = 20

Solving (2)

y_2 = 3 * 4

y_2 = 12

Hence;

B(x_2,y_2)= (20,12)

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