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A and B are two points on the x-axis and y-axis respectively. P (2, – 3) is the mid point of AB.

Find the equation of the line AB.

Answer:

**Solution:**

A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y.

Given, points A and B are on x-axis and y-axis respectively

Let co-ordinates of A be (x, 0) and of B be (0, y)

And P (2, -3) is the midpoint of AB

So, we have

2 = (x + 0)/2 and -3 = (0 + y)/2

x = 4 and y = -6

Equation of AB will be

y – y_{1} = m (x – x_{1})

y – (-3) = 3/2 (x – 2) [As P lies on it]

y + 3 = 3/2 (x – 2)

2y + 6 = 3x – 6

3x – 2y – 12 = 0

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