Question

Find the coordinates of the point that is
of the distance from C (-4, 1) to D (11,
6).

Answer 1

To find the coordinates, we first calculate the midpoint of the line segment CD, then apply the ratio to find the desired point.

Step-by-step explanation:

To find the coordinates of a point that is a certain distance away from another point, we can use the midpoint formula and the concept of ratios.

Let's calculate the midpoint of the line segment CD:

Midpoint formula:

(xm, ym) = ((x1 + x2) / 2, (y1 + y2) / 2)

Plugging in the coordinates of C (-4, 1) and D (11, 6), we get:

(xm, ym) = ((-4 + 11) / 2, (1 + 6) / 2) = (7/2, 7/2)

Now, to find a point that is 2/3 of the distance from C to D, we can use the concept of ratios. This point will be 2/3 of the way from C to the midpoint of CD. Applying the ratio to each coordinate, we get:

(x, y) = (-4 + (2/3)(7/2), 1 + (2/3)(7/2)) = (-4 + 7/3, 1 + 7/3) = (-5/3, 10/3)

Therefore, the coordinates of the point that is 2/3 of the distance from C to D are (-5/3, 10/3).

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