Question

Given segment AB with points (-4, 8) and (6,3) respectively. Find the

coordinates of point P that partitions Segment AB in the ratio 3:2. The answer should be entered in the form (x,y) with out any spaces between characters.

Answer 1

Answer:

The answer is "Coordinates of point P= (2,5)"

Step-by-step explanation:

We are familiar with the internal division of AB by point P, i.e. 3:2, $\frac{AP}{PB}= \frac{3}{2}$

Therefore, we use the internal division formula.

Points:

$\to (-4,8) \ and \ (6,3)\\\\ x_1 = -4\\y_1 = 8\\x_2= 6\\y_2 =3$

Formula:

$\to x = \frac{(mx_2 + nx_1)}{(m + n)}\\\to y = \frac{(my_2 + ny_1)}{(m + n)}\\\\where,\\\\\to m = 3 \\ \to n = 2$

Replacing the x coordinate representations of A and B with x, we have

$x = \frac{(3 \times 6 + 2 \times (-4))}{(3 + 2)}$

   $= \frac{(18 - 8)}{5}\\\\ = \frac{10}{5}\\\\ = 2$

Replacing the, y coordinate representations of A and B with y, we have

$y = \frac{(3 \times 3 + 2 \times 8)}{(3 + 2)}$

  $= \frac{( 9 +16)}{(5)}\\\\= \frac{25}{5}\\\\=5$

The coordinates of point P= (2,5).