CBSE Class 10 Maths Chapter 7 Important Questions with Solutions: Central Board of Secondary Education has released the model papers for its annual class 10th board examinations for the academic session 2022-23. Although the final CBSE Class 10th date sheet for 2023 has not been published by the board yet, the exams are likely to start from February 15, 2023. Thus, the students would have almost two months to prepare for their final examination.
When it comes to the individual papers, Mathematics is often dreaded amongst the student community. However, all it requires is regular practice to pass CBSE Class 10 board examination with flying colours.
In this article, we are going to discuss the important questions from Unit III, Chapter 7 Coordinate Geometry. It carries a total weightage of 06 marks covering topics such as Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula. View the Mathematics syllabus in detail by clicking on the link below.
CBSE Class 10 Maths Chapter 7 Important Questions
MULTIPLE CHOICE QUESTIONS
Q1. The distance of the point P (-6, 8) from the origin is:
Q2. 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, the value of k is:
Q3. The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ - b cos θ), is :
Q4. If the point P (k, 0) divides the line segment joining the points A (2, -2) and B (-7, 4) in the ratio 1:2, then the value of k is :
Q5. If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1, then the value of y is :
Q6. Distance between two points (3, 2) and (6, 6) is:
Q7. The line segment joining the points P (-3, 2) and Q (5, 7) is divided by the y- axis in the ratio:
(a) 3 : 1
(b) 3 : 2
(c) 3 : 4
(d) 3 : 5
Q8. The point P on x- axis is equidistant from the points A (-1, 0) and B (5, 0) is:
(a) (2, 2)
(b) (0, 2)
(c) (2, 0)
(d) (3, 2)
SHORT ANSWER TYPE QUESTION ( 2 MARKS)
Q1. Find the point on the x-axis which is equidistant from the points (2, -5) and (-2, 9)
Q2. Find the distance of the point P (2, 3) from the x-axis.
Q3. Find the ratio in which the point (-3, k) divides the line-segment joining the points (-5, 4) and (-2, 3). Also find the value of k.
Q4. If A (5,2), B (2, -2) and C (-2, t) are the vertices of a right-angled triangle with ∠B = 90°, then find the value of t.
Q5. In what ratio does the point P (2, -5) divide the line segment joining A (-3, 5) and B (4, -9).
SHORT ANSWER TYPE QUESTION ( 3 MARKS)
Q1. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Q2. Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
Q3. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.
Q4. If A (-2,1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.
Q5. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order find x and y.
LONG ANSWER TYPE QUESTIONS (4 MARKS)
Q1. The vertices of quadrilateral ABCD are A (5, -1), B (8,3), C (4, 0) and D (1, -4). Prove that ABCD is a rhombus.
Q2. Find the centre and radius of the circumcircle (i.e., circumcentre and circum-radius) of the triangle whose vertices are (-2, 3), (2, -1) and (4, 0).
Q3. Find the coordinates of the points of trisection (i.e., Points dividing in three equal parts) of the line segment joining the points A (2, -2) and B (-7, 4).
Q4. An equilateral triangle has one vertex at (3, 4) and another at (-2, 3). Find the co- ordinates of the third vertex.
Q5. The three vertices of a parallelogram ABCD are A (3, -4), B (-1, -3) and C (-6, 2). Find the coordinates of vertex D and find the area of ABCD.
Q6. The base QR of an equilateral triangle PQR lies on x-axis. The co-ordinates of point Q are (-4, 0) and the origin is the mid-point of the base. Find the co-ordinates of the point P and R.
Also test your preparation with these practise papers created by our subject experts to prepare the candidates of CBSE Class 10 Math Board Examination 2023.
All the best!