CBSE Class 10 Coordinate geometry Sure Shot Questions Set K

(2 MARKS QUESTIONS)

Question. What is the distance of the point P(2,3) from the X – axis?
Answer: 3 units

Question. A point \( a \) lies on the \( X \) axis, What is the coordinate of this point ?
Answer: \( (a, 0) \)

Question. Find the distance between P(7,5) and Q(2,5)
Answer: 5

Question. If the distance between the points (4,p) and (1,0) is 5, then find the value of p
Answer: \( \pm 4 \)

Question. Find the ratio in which the y -axis divides the segment joining (-3,6) and (12,-3)
Answer: \( 1/4 \)

Question. If the points A(x, 2), B(-3, 4) and C(7, -5) are collinear, then find the value of x
Answer: \( x = -63 \)

Question. In which quadrant the point P that divides the line segment joining the points A(2, -5) and B(5,2) in the ratio 2 : 3 lies?
Answer: 4 th Quadrant

Question. What is the mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4)?
Answer: (-4,2)

Question. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Answer: \( 3x + y – 5 = 0 \)

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

Question. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.
Answer: \( p = 7 \)

Question. Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units
Answer: \( y = 3, y = -9 \)

Question. Find the distance of the point P (−3, 4) from the origin.
Answer: 5

Question. If A and B are the points (−6, 7) and (−1, −5)respectively, then find the distance 2AB.
Answer: 26

Question. If P and Q are the points having coordinates (8, 3) and (5, −1) respectively, then find the distance 3PQ
Answer: 15

Question. If \( C (a, 3) \) is the mid-point of the line segment joining the points A(5, 4) and B(−3, 2),then find the value of \( a \)
Answer: 1

Question. If \( P (\frac{a}{2},4) \) is the mid-point of the line-segment joining the points A(−6, 5) and B(−2, 3), then find the value of \( a \).
Answer: \( -8 \)

Question. Find the point on the x-axis which is equidistant from points (−1, 0) and (5, 0)
Answer: (2, 0)

Question. ABCD is a rectangle whose three vertices are B (4, 0), C (4, 3)and D (0, 3).Find the length of one of its diagonals.
Answer: 5 units

Question. Find a relation between \( x \) and \( y \) such that the point \( (x, y) \) is equidistant from the points A(3, 6) and B (−3, 4)
Answer: \( 3x + y = 5 \)

(3 MARKS QUSETIONS)

Question. P \( (x, −3) \) and Q(3 , \( y \)) are points of trisections the line segment joining A(7, −2) and B (1, −5), then find the values of \( x \) and \( y \)
Answer: \( x = 5, y = -4 \)

Question. Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
Answer: Ratio is 1:1 and Coordinates: \( (-\frac{3}{2}, 0) \)

Question. Find the third vertex of a triangle, if its two vertices are(-3,1) and (0,-2) and the centroid of this triangle is at origin.
Answer: (3,-1)

Question. If P and Q are points of trisection of the line segment joining the points A(2,-2) and B(-7,4) such that P is nearer to A. Find the coordinates of P and Q
Answer: P(-1,0) and Q(-4,2)

Question. If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR.
Answer: \( \pm 4, QR = \sqrt{41}, PR = \sqrt{82}, 9\sqrt{2} \)

Question. Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Δ ABC. (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
Answer: \( D (\frac{7}{2}, \frac{9}{2}), P (\frac{11}{3}, \frac{11}{3}) \)

Question. Find the coordinates of a point A, where AB is a diameter of the circle with centre (3,-1) and the point B is (2,6)
Answer: (4, -8)

Question. If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that \( AP = \frac{3}{7}AB \) and P lies on the line segment AB.
Answer: \( (-\frac{2}{7}, \frac{20}{7}) \)

Question. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
Answer: Square

Question. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order. Also find the perimeter.
Answer: 24 sq units

Question. A point P(1 , \( a \)) is at a distance of 3 units from the point Q(1, 2) Find the value of \( a \)
Answer: \( a = 5 \) or \( -1 \)

Question. Find the value of y for which the distance between the points A (3, −1)and B (11, \( y \)) is 10 units.
Answer: \( y = 5 \) or \( -7 \)

Question. The length of a line segment is 10. If it’s one end is at (2, −3)and other end is at (10, \( y \)) then find the value(s) of y.
Answer: \( y = 3 \) or \( -9 \)

Question. The length of a line segment is 10. If one end is at (2, − 3)and the abscissa of the second end is 10. Find its ordinate.
Answer: \( y = 3 \) or \( -9 \)

Question. The point A(3, \( y \)) is equidistant from the points P(6, 5)and Q(0, − 3).Find the value of y.
Answer: 1

Question. Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1),B (−2, −4),C(4, −1) and D (3, 4).
Answer: 28 sq units

Question. Find the ratio in which point P(−1, \( y \)) lying on the line segment joining points A(−3, 10) and B (6, −8)divides it. Also find the value of y.
Answer: 2: 1, \( y = 6 \)

Question. Find the value of p, so that the point (p, 2) divides the line- segment joining the points (2, 5) and (4, 7).
Answer: \( p = -\frac{5}{3} \)

Question. Find the ratio in which the line segment joining the points A (3, −3) and B(−2, 7) is divided by x axis. Also find the coordinates of the point of division.
Answer: 7: 3, \( (-\frac{1}{2}, 0) \)

Question. Find a point P on the y- axis which is equidistant from the points A(4, 8) and B(−6, 6).Also find the distance AP.
Answer: (0, 2); \( 2\sqrt{13} \)

(5 MARKS QUESTIONS)

Question. If (1, 2),(4, \( y \)), (\( x \), 6)and (3, 5)taken in order, are the vertices of a parallelogram, then find the values of \( x \) and \( y \) .
Answer: \( x = 6, y = 3 \)

Question. If A (−2, −1), B (\( a \), 0), C(4, b)and D(1, 2)are the vertices of a parallelogram ABCD, find values of \( a \) and \( b \).
Answer: \( a = 1, b = 3 \)

Question. If A and B are (4, −3), and (8, 5), respectively the coordinates of a line segment AB, find the coordinates of a point P such that \( AP = \frac{3}{7}AB \), where P lies on AB.
Answer: \( (\frac{40}{7}, \frac{3}{7}) \)

Question. In what ratio, does the point (1, p)divides the line segment joining the points (−5, 1) and(4, −2)? Also find the value of \( p \)
Answer: 2: 1, \( p = -1 \)

Question. Point P divides the line segment joining the points A (2, 1)and B (5, −8) such that \( \frac{AP}{AB} = \frac{1}{3} \). If P lies on the line \( 2x − y + k = 0 \), find the value of k
Answer: \( -8 \)

Question. The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the value of p.
Answer: \( p = 7 \) or 4

Question. Find the coordinates of a point P on the line segment joining A (1, 2) and B(6 ,7) is such that \( AP = \frac{2}{5}AB \).
Answer: (3, 4)