Question

Grace has a segment with endpoints F (4.9) and G (7.2) that is divided by a point H such that FH and GH form a 1:3 ratio. She knows that the distance between the
x coordinates is 3 units. Which of the following fractions will let her find the x coordinate for point H?
1/4
1/3
3/4
3/1

Answer 1

The fraction used to find the x coordinate for point H is 1/4.

Distance

If a point O(x, y) is dividing the line segment AB with endpoints at A(x₁, y₂) and B(x₂, y₂) in the ratio n:m, hence:

$x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1$

For the question the fraction used = 1 / (1 + 3) = 1/4

The fraction used to find the x coordinate for point H is 1/4.

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