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# [Smart Math] Geometry Problem 3

Here’s and example of a SMART MATH problem for GEOMETRY.

### Problem

Find the coordinates of the point B if B divides A and C internally in the ratio of 2 : 3. Given that A (–3, –4) and C (2, –1).

1. $\frac{-14}{5},-1$
2. $-1,\frac{-14}{5}$
3. $1,\frac{-14}{5}$
4. $\frac{-1}{5},-14$
5. $1,\frac{14}{5}$

### The Usual Method

Let the coordinates of B be (x, y). Using the internal division formula, we get:

$x=\frac{2(2)+3(-3)}{2+3}=\frac{4-9}{5}=-1$

$y=\frac{2(-1)+3(-4)}{2+3}=\frac{-2-12}{5}=\frac{-14}{5}$

Hence, coordinates of B are

$-1,\frac{-14}{5}$

.

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.