Question

A point lies on AB¯¯¯¯¯ and is located 34 ​the distance from A to B.

What are the coordinates of this point?


(3, 2)

(4, 2)

(8, 2)

(9, 2)

Answer 1

The coordinates of the point located 34​ the distance from A to B are (206, 4).

Step-by-step explanation:

To find the coordinates of a point located a certain distance from point A to point B, we can use the formula:

x = (1 - t) * x(A) + t * x(B)

y = (1 - t) * y(A) + t * y(B)

where t is the distance ratio.

In this case, the distance ratio is 34.

Substituting the given coordinates of A(2, 4) and B(8, 4) into the formula, we get:

x = (1 - 34) * 2 + 34 * 8 = 2 * (1 - 34) + 8 * 34 = 2 - 68 + 272 = 206

y = (1 - 34) * 4 + 34 * 4 = 4 * (1 - 34) + 4 * 34 = 4 - 136 + 136 = 4

Therefore, the coordinates of the point located 34​ the distance from A to B are (206, 4).