# NCERT Class 10 Chapter 4 Coordinate Geometry Official CBSE Board Sample Problems Long Answer

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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 can’t 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

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:

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