Question

Find the coordinates of P so that P partitions the segment AB in the ratio 3:4 if A(-9, -9) and B(5, -2).

Answer 1

Using the section formula for internal division, the coordinates of point P that partitions the segment AB in the ratio 3:4, where A is (-9, -9) and B is (5, -2), are calculated to be (-1/7, -38/7).

Step-by-step explanation:

To find the coordinates of point P that partitions the segment AB in the ratio 3:4 where A(-9, -9) and B(5, -2), we will use the section formula for internal division. The formula for the x-coordinate is x = (mx2 + nx1) / (m + n), and for the y-coordinate is y = (my2 + ny1) / (m + n), where m:n is the given ratio and (x1,y1), (x2,y2) are the coordinates of A and B, respectively.

Applying the values we have:

• x-coordinate of P: (3(5) + 4(-9)) / (3 + 4) = (-1) / 7 = -1/7
• y-coordinate of P: (3(-2) + 4(-9)) / (3 + 4) = (-38) / 7 = -38/7

So, the coordinates of P are (-1/7, -38/7).