Ncert solutions mathematics class 10 Solutions for Chapter 7 coordinate geometry

Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the figure below. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Find the distance between (a, b), (- a, – b).

Name the type of quadrilateral formed by (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)

If Q (0, 1) is equidistant from P (5, – 3) and R (x, 6), find the values of x.

Name the type of quadrilateral formed by (- 3, 5), (3, 1), (0, 3), (- 1, – 4)

Name the type of quadrilateral formed by (4, 5), (7, 6), (4, 3), (1, 2)

If Q (0, 1) is equidistant from P (5, – 3) and R (4, 6), find the distance of QR and PR.

If Q (0, 1) is equidistant from P (5, – 3) and R (-4, 6), find the distance of QR and PR.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).

Find the distance between (2, 3), (4, 1).

Find the distance between (-5, 7), (-1, 3).

Find the distance between the points (0, 0) and (36, 15).

Find the values of y for which the distance between the points P (2, – 3) and Q (10, y) is 10 units.

Find the area of quadrilateral ABCD whose vertices are A(-3, 2), B(5, 4), C(7, -6), and D(-5, -4).

Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

Find the coordinates of the point which divides the line joining (- 1, 7) and (4, – 3) in the ratio 2:3.

Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, – 3) and B is (1,4).

Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

Find the ratio in which the line segment joining A (1, – 5) and B (- 4, 5) is divided by the x-axis.

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.

Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order.

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th the distance AD on the eighth line and posts a red flag. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Find the ratio in which the line segment joining the points (-3, 10) and (6, – 8) is divided by (-1, 6).

In (7, -2), (5, 1), (3, -k) find the value of ‘k’, for which the points are collinear.

In (7, -2), (5, 1), (3, -k) find the value of ‘k’, for which the points are collinear.

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Find the area of the triangle whose vertices are (2, 3), (-1, 0), (2, -4).

You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Check the same for ΔABC whose vertices are A (4, – 6), B (3, – 2) and C (5, 2).

Find the area of the triangle whose vertices are (-5, -1), (3, -5), (5, 2)

Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

The vertices of a ∆ ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that \frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}. Calculate the area of the ∆ ADE and compare it with area of ∆ ABC.

Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of ∆ ABC. The median from A meets BC at D. Find the coordinates of point D.

Points A (4, 2), B (6, 5) and C (1, 4) be the vertices of ∆ ABC. The median from A meets BC at D. Find the coordinates of the point P on AD such that AP : PD = 2 : 1.

If A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

Points A (4, 2), B (6, 5) and C (1, 4) be the vertices of ∆ ABC. Find the coordinates of point Q and R on medians BE and CF respectively such that BQ : QE = 2:1 and CR : RF = 2 : 1.

Find the relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).

ABCD is a rectangle formed by the points A (− 1, − 1), B (− 1, 4), C (5, 4) and D (5, − 1). P, Q, R and S are the mid-points of AB, BC, CD, and DA respectively. Is the quadrilateral PQRS is a square? A rectangle? Or a rhombus?

The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, –2) and B(3, 7).