Question

In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? Diagram shows a line segment with endpoints A(2, minus 6) and B(10, 2). Point D lies on this line segment. A dashed segment extends up from point A until point C and then extends horizontally to right until point D, forming a right triangle. A. (2, -1) B. (2, -3) C. (5, -3) D. (7, -1) Reset Next

Answer 1

The coordinates of point C that forms the triangle is; (2, -1)

How to partition a line segment?

We are told that point D divides line segment AB in the ratio of 5:3.

The line segment division formula is;

(x, y) = (m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)

For this question;

x₁ = 2; y₁ = -6; x₂ = 10; y₂ = 2; m₁ = 5; m₂ = 3

Thus, (x, y) gives us;

(5*10 + 3*2)/(5 + 3), (5*2 + 3*-6)/(5 + 3)

D(x, y) = (7, -1)

Now, we need to find the coordinates of C

We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line

And coordinate of y will be same as y in D since CD is horizontal line. Thus, coordinate of C is; C(2,-1).

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