Question

What is the x-coordinate of the point that divides the directed line segment from K to J into a ratio of 1:3?

A. (x₁ + 3x₂)/4
B. (3x₁ + x₂)/4
C. (x₁ + x₂)/2
D. (2x₁ + 2x₂)/3

Answer 1

The x-coordinate of the point that divides the directed line segment from K to J in a 1:3 ratio is given by the formula (3x₁ + x₂)/4, which corresponds to answer choice B.

Step-by-step explanation:

To find the x-coordinate of the point that divides a directed line segment from point K to point J in a 1:3 ratio, we can use the formula for the coordinates of a point that divides a line segment in a given ratio, which is often referred to as the section formula. In this case, if the coordinates of K are (x₁, y₁) and the coordinates of J are (x₂, y₂), the x-coordinate of the dividing point P in the ratio m:n is given by

(mx₂ + nx₁) / (m + n).

Here, the ratio is 1:3, so applying this to find the x-coordinate gives us:

(1x₂ + 3x₁) / (1 + 3) = (3x₁ + x₂)/4.

Therefore, the correct answer is B. (3x₁ + x₂)/4.