# NCERT Class 10 Chapter 4 Coordinate Geometry Official CBSE Board Sample Problems Long Answer (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Question

**The coordinates of the points A, B and C are** **and** **respectively. P (x, y) is any point in the plane. Show that**

### Solution

Taking points P, B, C. Firstly,

Area

sq. units

Now, area

sq. units

Hence,

## Question

**Prove that the area of a triangle with vertices** **and** **is independent of t**.

### Solution

Given vertices of triangle are

*Let* *)* are vertices of the triangle.

Area of the triangle

sq units, since area canีt be negative.

Hence, area is independent of t.

## Question

**Show that the points** **and** **are the vertices of the right angled triangle**.

### Solution

Let are the vertices of , by the distance formula,

Here

Hence is a right angled triangle at A.

## Question

**Determine the ratio in which the line** **divides the line segment joining the points** **and**.

### Solution

Let the line divide the line segment joining the points and at the point in the ratio k: 1.

Since this point of intersection lies on the line

Hence the required ratio is or 6: 25 externally

## Question

**Find the values of a and b if the points** **and** **are collinear and a- b = 1**

### Solution

Given that the points are collinear

Then the area of formed by points is equated to 0

also,

Solving these two equations we get, and

## Question

**If the points** **and** **are collinear and**, **then find the values of a and b**.

### Solution

If points are collinear, area of triangle is 0.

## Question

**Find the coordinates of the point R on the line segment joining the points** **and** **such that**

### Solution

We have

## Question

**Find the ratio in which the line** **divides the line segment joining the points** **and**. **Find the coordinates of the point of division**.

### Solution

Let the line , divide the line segment joining and in the ratio k: 1 at point P.

Coordinates of P must satisfy the equation of the line.

Hence we have:

The required ratio is 8: 1

Coordinates of P are: