Q. Find the coordinates of the centroid of a triangle.

  • Sol. Let the vertices of โˆ†ABC be A = (x1, y1), B = (x2, y2) and C = (x3, y3). Also, let the vertices of the centroid be G = (x, y).
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Q. Find the point on the X-axis which is equidistant from the points A(2, โ€“ 5) and B(โ€“ 2, 9).

Ans. (โ€“ 7, 0).

Q. Find the point on the Y-axis which is equidistant from the points (6, 5) and (โ€“ 4, 3).

Ans. (0, 9).

Q. If the point Q(0, 1) is equidistant from the points P(5, โ€“ 3) and R(x, 6), find the values of x. Also find the distances QR and PR.

  • Ans. x = ยฑ4, QR = โˆš41, PR = โˆš82 or โˆš92 units.

Q. Find the values of y for which the distance between the points P(2, โ€“ 3) and Q(10, y) is 10 units.

  • Ans. 3 or โ€“ 9.

Q. Name the quadrilateral formed by the following points A(4, 5), B(7, 6), C(4, 3) and D(1, 2).

  • Ans. Parallelogram.

Q. Find the equation of the perpendicular bisector of the line segment joining the points (7, 1) and (3, 5).

  • Ans. x โ€“ y = 2.

Q. Find the relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (โ€“ 3, 4).

  • Ans. 3x + y = 5.

Q. Find the coordinates of the points of trisection of the line segment joining the points A(2, โ€“ 2) and B(โ€“ 7, 4).

  • Ans. (โ€“ 1, 0) and (โ€“ 4, 2)

Q. If A and B are two points having coordinates (โ€“ 2, โ€“ 2) and (2, โ€“ 4) respectively, find the coordinates of P such that AP = 3/7 AB

  • Ans. (-2/7, 20/7).

Q. Find the coordinates of the points which divide the line segment joining A(โ€“ 2, 2) and B(2, 8) into four equal parts.

  • Ans. (-1,7/2),(0, 5), (1, 13/2).

Q. ABCD is a rectangle where A(โ€“ 1, โ€“ 1), B(โ€“ 1, 4), C(5, 4) and D(5, โ€“ 1) are the vertices. P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively. Is the quadrilateral PQRS a square or a rectangle or a rhombus ? Justify your answer.

  • Ans. Rhombus because all the sides of quadrilateral are equal and diagonals are not equal to each other.

Q. Find the ratio in which the point P(โ€“ 4, 6) divides the line segment joining the points A(โ€“ 6, 10) and B(3, โ€“ 8).

  • Ans. 2 : 7.

Q. Find the coordinates of a point A where AB is a diameter of a circle whose centre is (2, โ€“ 3) and B is (1, 4).

  • Ans. (3, โ€“ 10).

Q. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, โ€“ 1), (2, 1) and (0, 3). Find the ratio of the area of a triangle formed to the area of the given triangle.

  • Ans. 1 sq. units, 1 : 4.

Q. The vertices of โˆ†ABC are A = (4, 6), B = (1, 5) and C = (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively such that AD/AB= AE/AC=1/4. Calculate the area of โˆ†ADE and compare it with the area of โˆ†ABC.

  • Ans. 15/32 sq. units, 1 : 16.

Q. Find the area of the quadrilateral ABCD whose vertices are A(โ€“ 4, โ€“ 2), B(โ€“ 3, โ€“ 5), C(3, โ€“ 2) and D(2, 3).

  • Ans. 28 sq. units.