Q) The coordinates of the end points of the line segment AB are A(-2, -2) and B(2, -4). P is the point on AB such that BP = AB. Find the coordinates of point P.    

PYQ: Q 22 – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans: 

Step 1: Given are the two points:

🔹 Point A = (−2, −2)

🔹 Point B = (2, −4)

Now a point P somewhere on the line from A to B. Let’s try to estimate location of this point P.

From question, we are given that

BP = 4/7 of AB

Let’s understand it by breaking the whole path AB into 7 equal parts:

∵ BP takes up 4 parts of path AB

∴ AP takes up the remaining 3 parts.

∴ Point P divides the line in the ratio 3:4

Step 2: Now that we have division ratio, we will use the section formula:

We know that according to Section formula, if a point P(x, y) divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) in the ratio m : n, then the coordinates of P are given by: 

Here we have, points A (- 2, – 2) and point B (2, – 4) are the given points, and P divides AB in the ratio 3:4.

∴ x₁ = – 2, y₁ = – 2, x₂ = 2, y₂ = – 4, m = 3, and n = 4

Let’s substitute these values into the section formula, we get coordinates of point P as:

Therefore the coordinates of point P are .

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