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The two opposite vertices of a square are (-1, 2) and (3, 2) . Find the coordinates of the other two vertices.

Let us assume ABCD is a square, where A(-1,2) and B(3,2). And Point O is the point of intersection of AC and BD To Find Coordinate of points B... View Article

Construct the following quadrilateral: Quadrilateral ABCD AB = 4.5 cm BC = 5.5 cm CD = 4 cm AD = 6 cm AC = 7 cm

Solution The rough sketch of the quadrilateral ABCD can be drawn as per the steps given below (1) ∆ABC can be constructed by using the given... View Article

Construct the following quadrilateral: Quadrilateral LIFT. LI = 4 cm IF = 3 cm TL = 2.5 cm LF = 4.5 cm IT = 4 cm

Solution A rough sketch of the quadrilateral LIFT can be drawn as follows. (1) ∆ ITL can be constructed by using the given measurements as... View Article

ABCD is a quadrilateral in which AD = BC and DAB = CBA (see Fig.) . Prove that (i) ΔABD ΔBAC (ii) BD = AC (iii) ABD = BAC

Solution Given AD = BC and ∠ DAB = ∠ CBA To Prove (i) ΔABD ΔBAC (ii) BD = AC (iii) ABD = BAC. Proof AD = BC, And ∠ DAB = ∠ CBA. On... View Article

A matchbox measures 4 cm×2.5cm×1.5cm. What will be the volume of a packet containing 12 such boxes?

Given Dimensions of the matchbox l = 4cm, b = 2.5cm, h = 1.5cm Find out We have to find out the volume of a packet containing 12 such boxes... View Article

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Given The length of the minute hand of a clock is 14 cm Find out To find the Area of the swept middle hand in 5 minutes Solution Let us... View Article

How many numbers lie between squares of the following numbers? i) 12 and 13 ii) 25 and 26 iii) 99 and 100

Solution We know that in-between n2 and (n + 1)2, there exists 2n natural numbers (i) 12 and 13 24 Here, n is 12, 2n =... View Article

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

Given that, ABCD is a rhombus. AC and BD are its diagonals. To Prove AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well... View Article

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

Let us assume the coordinates of point A be (x, y). Mid-point of AB is (2, – 3), which is the centre of the circle. Coordinate of B = (1, 4)... View Article

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC) .

Solution ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD. Ar(ΔDAC) = ar(ΔDBC)... View Article

In Fig. X = 62°, XYZ = 54°. If YO and ZO are the bisectors of XYZ and XZY respectively of Δ XYZ, find OZY and YOZ.

∠X = 62°, ∠XYZ = 54° We know that the sum of the interior angles of the triangle is 180°. ∠X +∠XYZ... View Article

The distributions of below give a weight of 30 students of a class. Find the median weight of a student.

Weight(in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 Number of students 2 3 8 6 6 3 2 Solution: Class Interval Frequency Cumulative... View Article

In quadrilateral ACBD, AC = AD and AB bisect A (see Fig.) . Show that ΔABC ΔABD. What can you say about BC and BD?

Solution Given AC and AD are equal AC = AD and the line AB bisects ∠A. To Prove ∆ ABC ≅ ∆ ABD Proof Considering the two triangles ΔABC and... View Article

Construct the following quadrilateral: Quadrilateral JUMP. JU = 3.5 cm UM = 4 cm MP = 5 cm PJ = 4.5 cm PU = 6.5 cm

Solution The rough sketch of the quadrilateral JUMP can be drawn as follows. (1) ∆ JUP can be constructed by using the given measurements as... View Article

In Figure, two chords AB and CD intersect each other at the point P. Prove that : (i) ∆APC ~ ∆ DPB (ii) AP . PB = CP . DP

Given: chords AB and CD intersect each other at the point P. To prove: (i) Δ APC ~ Δ DPB (ii) AP.PB = CP.DP Proof: In ∆ABC and ∆DPB,... View Article

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