Question

MATHEMATICSDESCRIPTIVEI. ANSWER ANY TEN OF THE FOLLOWING: ( 2 Marks )[10X2=20]1.Subtract (-72) from (234)2.Verify a -(-b) = a + b for a =5 and b= 63.Find the product 12 x (-8) + 12 x (-92) by using suitable property.4.Find the quotient of (-108) ÷ (-6)5.The product of two integer is 320. Find the other integer, if oneof theintegers is (-8).6.Evaluate: 26 ÷ {(-14) +1}7.Simplify: 2 19x 58x 2 158.Find 56of 900 m9.Divide 130 by 13410.The thickness of a book having 240 pages is 5 14cm. Find the thickness of each page.11.Write the following decimal numbers in the expanded form:a)3.063b) 1008.2112.Find the product of the following:a)3.54 x 10b) 0.096 x 100013.Solve: 108 ÷ 1.2II. ANSWERANY SIX OFTHE FOLLOWING: (5 Marks)[6X5=30]1.In a set of 10 questions, 5 marks are awarded for every correct answer and (-2) for every wrong answer. Rohan gets four correct and six wrong answers. What is his final score?2.Simplify: {1024 ÷ (-32)} + {(-125) ÷ 5}
3

Answer 1

Answer:

Let the vertices of an isosceles right triangle be A(7,10), B(-2,5) and C(3,-4)

So by distance formula we have,

Distance between two points =

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

AB=

(−2−7)

2

+(5−10)

2

=

81+25

=

106

BC=

(3+2)

2

+(−4−5)

2

=

(25+81)

=

106

AC=

(3−7)

2

+(−4−10)

2

=

−16+196

=

212

∴AB=BC⇒ This implies that ABC is an isosceles triangle.

Also,

AB

2

+BC

2

=106+106=212

∴AB

2

+BC

2

=AC

2

(Pythagoras theorem)

Hence, proved

∴ Δ ABC is a right triangle (proved)