Class 10 Coordinate Geometry Previous Year Questions

    Q1:

    If the point C (-1, 2) divides internally the line segment joining the points A (2, 5) and B (x, y) in the ratio 3 : 4, find the value of x² + y².

    CBSE [2016]

    Medium

    Q2:

    The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

    CBSE [2009]

    Medium

    Q3:

    A line intersects y-axis and x-axis at point P and Q respectively. If R(2, 5) is the mid-point of the line segment PQ, then find the coordinates of P and Q.

    CBSE [2023]

    Easy

    Q4:

    Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that x = y

    CBSE [2023]

    Easy

    Q5:

    The line segment joining the points A(4, -5) and B(4, 5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P.

    CBSE [2023]

    Easy

    Q6:

    Assertion (A) : If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3), then the value of x is 2. Reason (R) : Centre of a circle is the mid-point of each chord of the circle.

    CBSE [2023]

    Easy

    Q7:

    Question Image

    Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. Based on the above information, answer the following questions: (i) Taking O as origin, coordinates of P are (–200, 0) and of Q are (200, 0). PQRS being a square, what are the coordinates of R and S ? (ii) (a) What is the area of square PQRS ? OR (b) What is the length of diagonal PR in square PQRS ? (iii) If S divides CA in the ratio K:1, what is the value of K, where point A is (200, 800) ?

    CBSE [2023]

    Medium

    Q8:

    Find the distance of the point (–1, 7) from x-axis.

    CBSE [2023]

    Easy

    Q9:

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

    CBSE [2023]

    Easy

    Q10:

    Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right-angles triangle.

    CBSE [2023]

    Easy

    Q11:

    The centre of a circle is (2a, a - 7). Find the value of 'a' if the circle passes through the point (11, -9). Radius of the circle is 5√2 cm.

    CBSE [2023]

    Easy

    Q12:

    If (-5, 3) and (5, 3) are two vertices of an equilateral triangle, then find the co-ordinates of the third vertex, given that the origin lies inside the triangle. (Take √3 = 1.7)

    CBSE [2023]

    Medium

    Q13:

    Assertion (A) : Point P(0, 2) is the point of intersection of y-axis with the line 3x + 2y = 4. Reason (R) : The distance of point P(0, 2) from x-axis is 2 units.

    CBSE [2023]

    Easy

    Q14:

    Find the distance between the points (0, 2√5) and (-2√5, 0)

    CBSE [2023]

    Easy

    Q15:

    In what ratio does x-axis divide the line segment joining the points A(3, 6) and B(-12, -3) ?

    CBSE [2023]

    Easy

    Q16:

    Draw a line segment AB of length 8 cm and locate a point P on AB such that AP : PB = 1 : 5

    CBSE [2022]

    Easy