Question

Suppose A, R, and B are collinear on AB, and AR:AB= 1/5. What are the coordinates of R?

Answer 1

R(1.6, 0)

Explanation:

Use the formula,
`(x, y) = (x_1 + k(x_2 - x_1), y_1 + k(y_2 - y_1))` to find the coordinates of point R, that partition the lie segment AB into the ratio 1/5.

Let,

`A(1, -1) = (x_1, y_1)`

`B(4, 4) = (x_2, y_2)`

Thus, plug in the values as follows:

`R(x, y) = (1 + (1)/(5)(4 - 1), -1 + (1)/(5)(4 -(-1))`

`R(x, y) = (1 + (1)/(5)(3), -1 + (1)/(5)(4 + 1)`

`R(x, y) = (1 + (1)/(5)(3), -1 + (1)/(5)(5)`

`R(x, y) = (1 + (3)/(5), -1 + (5)/(5))`

`R(x, y) = ((5 + 3)/(5), -1 + 1)`

`R(x, y) = ((8)/(5), 0)`

`R(x, y) = (1.6, 0)`

The coordinates of point R, are (1.6, 0)