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.

Triangle

Triangle

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

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:

Developed by: