Three friends Govind, Rishi and Kanika are participating in a Treasure Hunt organized in their school playground. The playground is mapped using a coordinate grid where each square represents 1 meter.
At a cerlain point in the game, they each stand at different spots waiting for their next clue. Their positions are recorded on the grid as points:
Govind is at point P
Rishi is at point Q
Kanika is at point R
The coordinate map is shown alongside.
Based on the above information, answer the following questions:
(i) Is Q the midpoint of segment PR? Justify your answer.
(ii) A new clue directs them to reach point M, which divides segment PQ in the ratio 2 : 3. Find the coordinates of M.

Question

Three friends Govind, Rishi and Kanika are participating in a Treasure Hunt organized in their school playground. The playground is mapped using a coordinate grid where each square represents 1 meter.
At a cerlain point in the game, they each stand at different spots waiting for their next clue. Their positions are recorded on the grid as points:
Govind is at point P
Rishi is at point Q
Kanika is at point R
The coordinate map is shown alongside.
Based on the above information, answer the following questions:
(i) Is Q the midpoint of segment PR? Justify your answer.
(ii) A new clue directs them to reach point M, which divides segment PQ in the ratio 2 : 3. Find the coordinates of M.

KnowledgeBoat · Accepted Answer

(i) From graph, Coordinates of P = (4, 13), Q = (7, 8) and R = (11, 2) By mid-point formula, Mid-point = Substituting values we get : Hence, Q is not the midpoint of segment PR. (ii) Given, M divides PQ in the ratio 2 : 3. By section formula, M = Substituting values we get : Hence, M = .

Mathematics

Section Formula

Related Questions

If the abscissa of a point P is 2, find the ratio in which this point divides the line segment joining the points (-4, 3) and (6, 3). Also, find the co-ordinates of point P.

Find the image of the point A(5, -3) under reflection in the point P(-1, 3).

M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3. Find :
(i) co-ordinates of M
(ii) co-ordinates of P
(iii) length of BP

A(3, 1), B(y, 4) and C(1, x) are vertices of triangle ABC and G(3, 4) is its centroid. Find the values of x and y. Also, find the length of side BC.