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AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is (A) 5 (B) 3 (C) √34 (D) 4

The correct answer is (C) √34 The three vertices are: A = (0, 3), O = (0, 0), B = (5,... View Article

The distance between the points (0, 5) and (-5, 0) is (A) 5 (B) 5√2 (C) 2√5 (D) 10

The correct answer is (B) 5√ 2 Solution We know that, Distance formula is given by d2 = (x2 – x1)2 + (y2 – y1)2... View Article

The distance of the point P (-6, 8) from the origin is (A) 8 (B) 2√7 (C) 10 (D) 6

Answer: (C) 10 Distance between two points can be evaluated if we know the coordinates of the two points in the... View Article

The distance between the points A (0, 6) and B (0, -2) is (A) 6 (B) 8 (C) 4 (D) 2

The correct answer is (B) 8 Solution We know that, Distance formula is given by d2 = (x2 – x1)2 + (y2 – y1)2... View Article

The distance of the point P (2, 3) from the x-axis is (A) 2 (B) 3 (C) 1 (D) 5

The correct answer is (B) 3 Solution We know that, (x, y) is a point on the Cartesian plane in the... View Article

A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

Solution Let MN = 18 m be the flag pole and its shadow be LM = 9.6 m. The distance... View Article

For going to a city B from city A, there is a route via city C such that AC⊥CB, AC = 2 x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.

Answer According to the given details AC⊥CB, AC = 2x km, CB = 2 (x + 7) km and AB =... View Article

A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.

Solution Let the length of the ladder = AC = 5 m Let the height of the wall on which... View Article

In Fig 6.17, if PQRS is a parallelogram and AB||PS, then prove that OC||SR.

Given According to the given details PQRS is a parallelogram, Therefore, PQ || SR and PS || QR. Also given, AB... View Article

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

Answer Given ∆ABC in which a line DE parallel to BC intersects AB at D and AC at E. To... View Article

It is given that ∆ ABC ~ ∆ EDF such that AB = 5 cm, AC = 7 cm, DF= 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.

Solution: According to the given details ∆ABC ∼ ∆EDF From the property of a similar triangle, We know that the corresponding sides of... View Article

In Fig. 6.16, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.

Solution: According to the given data ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm CP... View Article

If ∆ABC ∼ ∆DEF, AB = 4 cm, DE = 6, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆ABC.

Solution: According to the given details AB = 4 cm, DE = 6 cm EF = 9 cm FD = 12... View Article

Find the altitude of an equilateral triangle of side 8 cm.

Solution Let us consider ABC as an equilateral triangle of side 8 cm AB = BC = CA = 8... View Article

In figure, if AB || DC and AC, PQ intersect each other at the point O. Prove that OA.CQ = 0C.AP.

Solution According to the given details AC and PQ intersect each other at the point O and AB||DC. From ∆AOP... View Article

Diagonals of a trapezium PQRS intersect each other at the point 0, PQ || RS and PQ = 3 RS. Find the ratio of the areas of Δ POQ and Δ ROS.

Solution According to the given data PQRS is a trapezium in which PQ‖RS and PQ = 3RS PQ/RS = 3/1 =... View Article

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