Question

Segment AB in the coordinate plane has endpoints with coordinates A(5, 4) and B(−10,−6). Graph AB and find/plot two points C and D, so that they divide AB into two parts with lengths in a ratio of 2:3. Also, provide the coordinates of the points of partition. Coordinates of point C: Coordinates of point D:

Answer 1

First, we are going to plot the segment AB as:

Then, to find the coordinates that divide AB into 2 parts, we need to find the distance in the x-coordinate and the distance in the y-cordinate from points B to A as:

Distance x-coordinate = 5 - (- 10) = 5 + 10 = 15

Distance y-coordinate = 4 - (-6) = 4 + 6 = 10

So, we can calculate the distance from B to the partition points using the ratio as:

`\begin{gathered} \text{Distance x1 =}(2)/(2+3)(15)=6 \\ \text{Distance x2 =}(3)/(2+3)(15)=9 \\ \text{Distance y1 =}(2)/(2+3)(10)=4 \\ \text{Distance y2 = }(3)/(2+3)(10)=6 \end{gathered}`

So, the coordinates of points C and D can be calculated as:

C = B + (distance x1, distance y1)

D = B + (distance x2, distance y2)

Replacing, we get:

C = (-10, -6) + (6, 4) = (-10+6, -6 + 4) = (-4, -2)

D = (-10, -6) + (9, 6) = (-10+9, -6 + 6) = (-1, 0)

Answer: C(-4, -2)

D(-1, 0)