NCERT solutions for Mathematics Exemplar Class 10 chapter 7 - Coordinate Geometry [Latest edition]

The distance of the point P(2, 3) from the x-axis is ______.

The distance between the points A(0, 6) and B(0, –2) is ______.

The distance of the point P(–6, 8) from the origin is ______.

The distance between the points (0, 5) and (–5, 0) is ______.

AOBC is a rectangle whose three vertices are vertices A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.

The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is ______.

The points (–4, 0), (4, 0), (0, 3) are the vertices of a ______.

The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the ______.

The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.

The fourth vertex D of a parallelogram ABCD whose three vertices are A(–2, 3), B(6, 7) and C(8, 3) is ______.

If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.

If `P(a/3, 4)` is the mid-point of the line segment joining the points Q(– 6, 5) and R(– 2, 3), then the value of a is ______.

The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at ______.

The coordinates of the point which is equidistant from the three vertices of the ∆AOB as shown in the figure is ______.

A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle is ______.

A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively ______.

The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is ______.

If the distance between the points (4, p) and (1, 0) is 5, then the value of p is ______.

If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then ______.

∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0) E(4, 0) and F(0, 4).

Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).

The points (0, 5), (0, –9) and (3, 6) are collinear.

Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).

Points A(3, 1), B(12, –2) and C(0, 2) cannot be the vertices of a triangle.

Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.

A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).

Point P(5, –3) is one of the two points of trisection of the line segment joining the points A(7, – 2) and B(1, – 5).

Points A(–6, 10), B(–4, 6) and C(3, –8) are collinear such that AB = `2/9` AC.

The point P (–2, 4) lies on a circle of radius 6 and centre C (3, 5).

The points A(–1, –2), B (4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.

Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).

Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, –4). How many such points are there?

What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?

Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.

Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?

Find the coordinates of the point Q on the x-axis which lies on the perpendicular bisector of the line segment joining the points A(–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.

Find the value of m if the points (5, 1), (–2, –3) and (8, 2m) are collinear.

If the point A(2, – 4) is equidistant from P(3, 8) and Q (–10, y), find the values of y. Also find distance PQ.

Find the area of the triangle whose vertices are (–8, 4), (–6, 6) and (–3, 9).

In what ratio does the x-axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.

Find the ratio in which the point `P(3/4, 5/12)` divides the line segment joining the points `A(1/2, 3/2)` and B(2, –5). 

If P(9a – 2, –b) divides line segment joining A(3a + 1, –3) and B(8a, 5) in the ratio 3:1, find the values of a and b.

If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.

The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, –9) and has diameter `10sqrt(2)` units

The line segment joining the points A(3, 2) and B(5,1) is divided at the point P in the ratio 1:2 and it lies on the line 3x – 18y + k = 0. Find the value of k.

If `D((-1)/2, 5/2), E(7, 3)` and `F(7/2, 7/2)` are the midpoints of sides of ∆ABC, find the area of the ∆ABC.

The points A(2, 9), B(a, 5) and C(5, 5) are the vertices of a triangle ABC right angled at B. Find the values of a and hence the area of ∆ABC.

Find the coordinates of the point R on the line segment joining the points P(–1, 3) and Q(2, 5) such that PR = `3/5` PQ.

Find the values of k if the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear.

Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1). Also find the coordinates of the point of division.

If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

A(6, 1), B(8, 2) and C(9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ∆ADE.

The points A(x₁, _y1), B(x₂, y₂) and C(x₃, y₃) are the vertices of ∆ABC. The median from A meets BC at D. Find the coordinates of the point D.

The points A(x₁, _y1), B(x₂, y₂) and C(x₃, y₃) are the vertices of ∆ABC. Find the coordinates of the point P on AD such that AP : PD = 2 : 1

The points A(x₁, _y1), B(x₂, y₂) and C(x₃, y₃) are the vertices of ∆ABC.  Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1

The points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are the vertices of ∆ABC. What are the coordinates of the centroid of the triangle ABC?

If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.

Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?

Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.