Find the coordinates of P so that P partitions the segment AB in the ratio 6:2 if A(−4,12) A ( − 4 , 12 ) and B(9,−4) B ( 9 , − 4 )

Answer 1

Hi Pragnya,

There are many ways to approach this. Here is one way. I will list out the steps you need to take first. I recommend you try to follow the steps on your own before reading the answer below.

1. plot points A and B on an xy coordinate graph
2. draw a right triangle ABC with a right angle at point C
3. subract the x coordinates of A and B to get the length of the triangles base BC
4. since you need a ratio of 6:2, divide the length of AB by 8 (which is 6+2). Then multiply that value by 2
5. put your pen/pencil on point A, move towards the right as much as your answer in step 4, and draw a vertical line through the triangle. Where the line intersects segment AB we can label point P
6. to get the y value, repeat steps 3-5 using segment AC instead.

——————ANSWER BELOW——————

1. sorry can’t draw here
2. i drew triangle ABC with point C at (-4,-4)
3. length BC = 9 - (-4) = 13
4. 13 * 2/8 = 26/8 = 4.25
5. x coordinate of point P = -4 + 4.25 = 0.25
6. length AB = 12 - (-4) = 16

16 * 2/8 = 32/8 = 4

y coordinate of point P = 12 - 4 = 8

Answer: coordinate if point P = (0.25,8)

Note 1: the question doesn’t specify, so you also could have used point B instead of A for step 5, and gotten the coordinates P = (4.75,0)

Note 2: this method helps understand visually what’s happening, but a faster algebraic method to get the same answer is as follows-

1. B - A = (9,-4) - (-4,12) = (13, -16)
2. (13,-16) * 2/8 = (26/8,-32/8) = (4.25,-4) = L
3. P = A + L = (-4,12) + (4.25,-4) = (0.25,8)