Question

Point P divides the directed segment from A to B in the ratio 9 to 2. The coordinates of point A are

Answer 1

Answer:

$B =(3.3,1.7)$

Step-by-step explanation:

Given

$A(x_1,y_1) = (-4,-2)$

$P(x,y) = (2,1)$

$m : n = 9 : 2$

Required

The coordinates of $B(x_2,y_2)$

The line segment from ratio is calculated as:

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

Substitute: A, P, m and n

$(2,1) = (\frac{9 * x_2 + 2*-4}{9+2},\frac{9*y_2 +2 *-2}{9+2})$

$(2,1) = (\frac{9x_2 -8}{11},\frac{9y_2 -4}{11})$

Multiply through by 11

$(22,11) = (9x_2 -8,9y_2 -4)$

By comparison:

$9x_2 - 8 = 22$

$9y_2 - 4 = 11$

So, we have:

$9x_2 - 8 = 22$

$9x_2 = 22 +8$

$9x_2 = 30$

Solve for x2

$x_2 = 30/9$

$x_2 = 3.3$

$9y_2 - 4 = 11$

$9y_2 = 11+4$

$9y_2 = 15$

Solve for y2

$y_2 =15/9$

$y_2 =1.7$

So, the coordinates of B is:

$B =(3.3,1.7)$