Solution of Chapter 7. Coordinate Geometry (NCERT - Exemplar Mathematics Book)

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

If AOBC is a rectangle whose three vertices are A (0, 3), O (0, 0) and B (5, 0), then 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) and (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 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 ΔAOB as shown in the figure is

If a circle drawn with origin as the center passes through then 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), B (0, 0) and C (a, b) are collinear, then

ΔABC with vertices A(0 - 2, 0), B(2, 0) and C(0, 2) is similar to ΔDEF with vertices D( - 4, 0), E(4, 0) and F(0, 4).

The 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).

The points A (3, 1), B (12, - 2) and C (0, 2) cannot be vertices of a triangle.

The points A (4, 3), B (6, 4), C (5, - 6) and D ( - 3, 5) are vertices of a parallelogram.

A circle has its center 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 the line segment joining the points P (5, - 3) and Q (0, 4).

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

The points A ( - 6, 10), B ( - 4, 6) and C (3, - 8) are collinear such that

The point P ( - 2, 4) lies on a circle of radius 6 and center (3, 5).

The points A ( - 1, - 2), B (4, 3), C (2, 5) and D ( - 3, 0) are 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 from the point (7, - 4). How many such points are there?

What type of 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 point 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), then find the value 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 points of division.

Find the ratio in which the point divides the line segment joining the points

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

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

If the center of a circle is (2a, a – 7) then find the values of a, if the circle passes through the point (11, - 9) and has diameter 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 and are the mid - points of sides of ΔABC, then find the area of the ΔABC.

If the points A(2, 9), B(a, 5) and C(5, 5) are the vertices of a ΔABC right angled at B, then find the values of a and hence the area of ΔABC.

Find the coordinates of the point R on the line segment joining the points P(-1, 3) and Q(2, 5) such that

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, then 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 mid - point of DC, then find the area of ΔADE.

The points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are the vertices of ΔABC.

(i) The median from A meets BC at D. Find the coordinates of the point D.

(ii) Find the coordinates of the point P on AD such that AP: PD = 2: 1.

(iii) 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.

(iv) What are the coordinates of the centroid of the ΔABC?

If the points A(1, - 2), B(2, 3), C(a, 2) and D( - 4, - 3) form a parallelogram, then 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 distance 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.