Question

If the join of A (2,3) and B (4,6) is divided by P in such a way that PA : PB = 3:2 then find P.

A. P (3,4)
B. P (2.5, 4.5)
C. P (2.67, 4.67)
D. P (2.75, 4.75)

Answer 1

The coordinates of point P that divides the join of A (2,3) and B (4,6) in the ratio 3:2 are calculated using the section formula, resulting in P (3.2, 4.8), which is not provided in the options.

Step-by-step explanation:

The student is asking to find the point P that divides the join of A (2,3) and B (4,6) in the ratio of 3:2 respectively. This can be found using the section formula. According to the section formula for a line segment AB divided by a point P in the ratio m:n,

P(x, y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))

Applying this formula with A (2,3), B (4,6), and PA:PB = 3:2, we calculate the coordinates of P as follows:

P(x, y) = ((3*4 + 2*2) / (3 + 2), (3*6 + 2*3) / (3 + 2))

P(x, y) = (12 + 4)/(3 + 2), (18 + 6)/(3 + 2)

P(x, y) = (16/5, 24/5) = (3.2, 4.8)

Therefore, the correct answer is not listed among the given options. The calculated point P (3.2, 4.8) should be the point that divides the join of A and B in the given ratio.