Coordinate Geometry — Class 10 solved problems

44 problems from this chapter, each solved step by step.

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by the point (-1, 6).
The line segment is divided in the ratio 2:7.
Find a point on the y-axis that is at the same distance from the points (-5, 2) and (9, -2).
The point on the y -axis equidistant from (-5, 2) and (9, -2) is (0, -7).
Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.
The coordinates of the point are (7, 3).
Find the relation between x and y if the point (x, y) is equidistant from (7, 1) and (3, 5).
The relation between x and y is x - y = 2.
1. Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b)
(i) 2√2 units (ii) 4√2 units (iii) 2√(a² + b²) units
Find the coordinates of the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).
The coordinates of the points of trisection are P(-1, 0) and Q(-4, 2).
Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis, and find the coordinates of the point of division.
The ratio is 1:1 and the coordinates of the point of division are (-(3)/(2), 0).
Find the coordinates of a point P(x, y) lying on the line 2x + y = 6 such that the sum of its distances from the fixed points A(1, 1) and B(4, 5) is minimized
The coordinates of point P are ((59)/(20), (1)/(10)).
If (1,2), (4,y), (x,6), and (3,5) are the vertices of a parallelogram taken in order, find x and y.
The values are x=6 and y=3.
If point A(x, y) is equidistant from B(3, 6) and C(-3, 4), find a direct linear relation connecting x and y.
The linear relation connecting x and y is 3x + y - 5 = 0.
The line segment joining the points A(3, 2) and B(6, -7) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line 2x - y + k =
The value of k is -9.
The line segment joining the points A(2, 1) and B(5, -8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line 2x - y + k =
The value of k is -8.
The vertices of a triangle are A(-3, 5), B(7, 1), and C(3, 9). 1. Find the coordinates of the midpoint M of BC. 2. Show that AM is not a median of an equilatera
1. The coordinates of the midpoint M of BC are (5, 5). 2. The lengths of the sides are AB = √116, BC = √80, and AC = √52. Since the side lengths are not equal,
The vertices of a triangle are A(5, -1), B(-3, -2), and C(1, 8). Find the length of the median drawn from vertex A to side BC, and determine the coordinates of
The length of the median drawn from vertex A to side BC is 2√13 units, and the coordinates of the centroid of ABC are (1, (5)/(3)).
If the points A(x, y), B(2, 4), and C(4, 2) are vertices of a triangle whose area is 9 sq. units, show that: x+y=15 or x+y=-3
The relationships are x+y=15 or x+y=-3.
If the points A(x, y), B(1, 3), and C(3, 1) are vertices of a triangle whose area is 8 sq. units, show that: x+y=12 or x+y=-4
The relationship between x and y is x+y=12 or x+y=-4.
If the points A(x, y), B(2, 3), and C(3, 2) are vertices of a triangle whose area is 7 sq. units, show that: x+y=19 or x+y=-9
The relationship between x and y is x+y=19 or x+y=-9.
If the points A(x, y), B(1, 2), and C(2, 1) are vertices of a triangle whose area is 6 sq. units, show that: x+y=15 or x+y=-9
x+y=15 or x+y=-9
Find the coordinates of the point dividing the line segment joining A(3, 5) and B(9, 11) internally in the ratio 2: 1.
The coordinates of the point dividing the line segment are (7, 9).
Find the coordinates of the point that divides the line segment joining P(1, 2) and Q(7, 8) internally in the ratio 1: 2.
The coordinates of the point are (3, 4).
Find the distance between the points A(5, 9) and B(3, 11).
The distance between the points A(5, 9) and B(3, 11) is 2√2 units.
Determine if the vertices A(3, 1), B(6, 4), C(8, 2), and D(5, -1) form a specific quadrilateral (like a rectangle, rhombus, or square), and find its perimeter.
The given vertices form a rectangle, and its perimeter is 10√2 units.
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3:1 internally.
The coordinates of the point are (7, 3).
Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of the city from where bank, hospital, post office and superm
(i) The distance between the bank and the hospital is 13 units. (ii) The coordinates of the post office (E) are (7, 0). (iii) (a) The distance Partha needs to c
A line segment joining the points P(-5, 11) and Q is divided internally by the point M(2, -3) such that PM: MQ = 7: 2. The coordinates of Q are:
The coordinates of Q are (4, -7).
The point on x-axis which is equidistant from the points (5, -3) and (4, 2) is
(7, 0)
Find the ratio in which the point (-1, k) divides the line segment joining the points (-3, 10) and (6, -8). Hence, find the value of k.
The point (-1, k) divides the line segment in the ratio 2:7, and the value of k is 6.
(a) Show that the points ( -3, 3), (3, -3) and (3√3, 3√3) are the vertices of an equilateral triangle. OR (b) Prove that A(4, 3), B(6, 4), C(5, 6), D(3, 5) are
The points A(4, 3), B(6, 4), C(5, 6), D(3, 5) are the vertices of a square ABCD.
The coordinates of the point A, where AB is the diameter of the circle whose centre is (3, 2) and B (7, 4) is:
The coordinates of point A are (-1, 0).
The distance of the point (4, 7) from the x-axis is:
7 units
(a) Find the relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5). OR (b) Find the coordinates of the points
The relation between x and y is x - y = 2.
In the coordinate plane, triangle ABC is equilateral with B(1,0) and C(3,0). A line through the origin O meets AB and AC at M and N, respectively. If OM=MN, fin
The coordinates of M are ((5)/(4), (√3)/(4)).
Let the area of a PQR with vertices P(5, 4), Q(-2, 4) and R(a, b) be 35 square units. If its orthocenter and centroid are O(2, (14)/(5)) and C(c, d) respectivel
3
Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).
The relation between x and y is y = x - 2 or x - y - 2 = 0.
Do the points (3, 2), (-2, -3) and (2, 3) form a triangle? If so, name the type of triangle formed.
Yes, the points (3, 2), (-2, -3) and (2, 3) form a right-angled triangle.
x और y में एक संबंध ज्ञात कीजिए, ताकि बिंदु (x, y) बिंदुओं (7, 1) और (3, 5) से समदूरस्थ (equidistant) हो।
निकला हुआ संबंध है x - y = 2।
Find a point on the y -axis which is equidistant from the points A(6, 5) and B(-4, 3).
The point on the y -axis equidistant from A(6, 5) and B(-4, 3) is (0, 9).
Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (-2, -5) and (6, 3). Find the coordinates of the point of intersection.
The line x - 3y = 0 divides the line segment in the ratio 13:3. The coordinates of the point of intersection are ( (9)/(2), (3)/(2)).
If the coordinates of the mid-points of the line joining the points (3a, 4) and ( - 2, 2b) are (5, a), then
The values are a = 4 and b = 2.
In the coordinate plane, triangle ABC is equilateral with B(1, 0) and C(3, 0). A line through the origin O meets AB and AC at M and N respectively. If OM = MN,
The coordinates of M are (5/4, √3/4).
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence, find m.
The ratio is 1:1 and m=0.
The coordinates of a point on the x-axis, which is equidistant from ( - 2, 5) and (2, - 3) are:
(-2, 0)
Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1).
The area of the triangle is 30.5 square units.
Find the distance between the parallel lines 3x + 4y - 7 = 0 and 3x + 4y + 23 = 0.
The distance between the parallel lines is 6 units.

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