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).
The Usual Method
Let the coordinates of B be (x, y). Using the internal division formula, we get:
Hence, coordinates of B are
Estimated Time to arrive at the answer = 45 seconds.
If a line is cut by a point in a certain ratio, then its length along the X-axis and that along the Y-axis is also cut in the same ratio.
In this case, the x coordinate of A (–3) and that of C (2) are –3 –2 = –5 or 5 units apart along the X-axis. When this has to be divided in the ratio of 2 : 3; 2 parts towards point A and 3 parts towards point C, we get the coordinate of point B.
As can be seen in the above figure; the value of x coordinate of point B will be –1 (2 units on the right of –3 or 3 units on the left of 2). Once we know that the x coordinate is –1, we can look at the options and see that only option ‘2’ satisfies the requirement and hence the answer should be option ‘2’.
Estimated Time to arrive at the answer = 10 seconds.