CBSE Class 10 Mathematics Coordinate Geometry VBQs

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

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. 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. 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 =37 AB, where P lies on AB.
Answer : (40/7, 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. Find the coordinates of a point P on the line segment joining A (1, 2) and B (6 ,7) is such that AP = 2/5 AB.
Answer : (3,4)

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: (−3/2 ,0)

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. 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 : ±4 ,𝑄𝑅= √41, 𝑃𝑅= √82, 9√2

Question. Determine, whether each of the given points (-2,1), (2,-2) and (5,3) are vertices right angles.
Answer : Do yourself

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. 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 : (7/2, 9/9) , P (11/3, 11/3)

Question. Show that the points(−2,5), (3,−4) and (7,10) are the vertices of a right triangle.
Answer : Do yourself

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. 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,(−1/2,0)

Question. If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = 37 AB and P lies on the line segment AB.
Answer : (−2/7 ,20/7)

Question. There are two routes to travel from source A to destination B by bus. First bus reaches at B via point C and second bus reaches from A to B directly. If coordinates of A, B and C are(-2, -3), (2, 3) and (3, 2) respectively then by which bus do you want to travel from A to B (Assume that both buses have same speed.) Which value isdepicted in the question?
Answer : By direct route from A to B. Reasoning, Time saving, Economical

Question. In a sports day celebration, Ram and Shyam are standing at positions A and B whose coordinates are (2, -2) and (4, 8) respectively. The teacher asked Geeta to fix the country flag at the mid point of the line joining points A and B. Find the coordinates of the mid point? Which type of value would you infer from the question?
Answer : (3, 3), Enjoyment, Reasoning.

Question. To raise social awareness about hazards of smoking, a school decided to start "No Smoking" campaign. 10 students are asked to prepare campaign banners in the shape of triangle as shown in the fig. If cost of 1 cm2 of banner is Rs.2 then find the overall cost incurred on such campaign. Which value is depicted in the question?

Answer : Rs. 300, Social awareness

Question. The coordinates of the houses of Sameer and Rahim are (7, 3) and (4, -3) whereas the coordinates of their school is (2, 2). If both leaves their houses at the same time in the morning and also reaches school on time then who travel faster? Which value is depicted in the question?
Answer : Samir, Punctuality, Sincerity.

Question. There are two types of fields are available as shown in the fig. which type of field will you purchase if both have same cost? Which value is depicted in the question?

Answer : Rectangular, Economical

CASE STUDY - 1

Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the fig. The students are to sow seeds of flowering plants on the remaining area of the plot.

(i) What are the coordinates of P?
Answer : (4, 6)

(ii) What are the coordinates of D?
Answer : (16, 0)

(iii) Find the coordinates of P if D is taken as origin
Answer : (-12, 6)

CASE STUDY - 2

Seema has a 10 m × 10 m kitchen garden attached to her kitchen. She divides it into a 10 ×10 grid and wants to grow some vegetables and herbs used in the kitchen. She puts some soil and manure in that and sow a green chilly plant at A, a coriander plant at B and a tomato plant at C. Her friend Kusum visited the garden and praised the plants grown there. She pointed out that they seem to be in a straight line. See the below diagram carefully and answer the following questions:

(i) Find the distance between A and B is
Answer : √13

(ii) Find the mid- point of the distance AB
Answer : (3.5, 3)

(iii) Find the distance between B and C
Answer : 2√2