Question Pool Geometry and Algebra

# Geometry and Algebra - SAMAGRA Question Pool & Answers | Class 10 English Medium

Kerala Syllabus SAMAGRA SCERT SAMAGRA Question Pool for Class 10 English Medium Maths Geometry and Algebra

Qn 1.

(a) Find Slope of the line passing through ( 3 ,5 ) , ( 4 , 7 ).

(b) What is the slope a line parallel to this line ?

a) Slope = 2

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Qn 2.

Write the equation of the line passing through A ( 0 ,12) and B ( 16 , 0)

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Qn 3.

The vertices of a triangle are ( -3 , 3 ) , ( 5 , 3 ) and ( 1 , 6 ) . Prove that it is an isosceles triangle

Lengths of sides are 8, 5, 5

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Qn 4.

Consider the points A ( 1, 0 ) , B ( 7 , 0 ) C ( 4 , 4 )

a). Which of these points are on the x - axis ?

b). Prove that triangle ABC is isosceles.

a) A (1 , 0), B (7 ,

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Qn 5.

Consider the points L ( 9, 2) and M (1 , -2)

a). What is the slope of the line LM ?

b). Find the coordinates of two more points on the line

c). Find the coordinates of the point where this line meets the x - axis

(a) slope =

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Qn 6.

If A (2,3) and B (6,9) are two points on a line , then

(a) Find the coordinates of the mid point of the line AB

(b) Find the slope of AB

(c) Find the equation of the line having slope and passing through the mid point of AB.

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Qn 7.

P (5 , 2), Q (8 , 6) are two points on a line, then

a). What is the slope of PQ?

b). Write the equation of the line PQ

c). Find the co-ordinates of the point at which the line PQ cut the 'x' axis

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Qn 8.

If the equation of a circle is x2+y2=4 then

(a)What is the radius of the circle ?

(b) If the x coordinate of a point on this  circle is zero, what is the y- coordinate of that point ?

(c) Write the coordinates of another point on the circle.

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Qn 9.

A circle with centre at (1,3) passes through the point  (5,6).

(a) Find the radius of the circle?

(b) Write the equation of the circle.

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Qn 10.

A (2,5) and B (a,-3) are joined to get the line AB as in the figure and P (4,b) is the mid point of AB.

a) Find the value of a .

b) Find the value of b .

a) a =

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Qn 11.

The equation of a circle is x2+y2=9

(a) Find the radius of the circle ?

(b) Write the coordinates of the centre of the circle .

(c) Find the points of contact of the circle with X axis.

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Qn 12.

A (2,3) B (6,7) are two points on a line .

(a) Find the slope of AB.

(b) If P is the mid point of AB , then find the coordinates of P.

(c) Write the equation of the line AB.

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Qn 13.

In the figure PB : QB = 1 : 2. Find the coordinates of the point B

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Qn 14.

In the figure, OC is perpendicular to AB.

(a) Prove that Δ OAB is isosceles ?

(b) Find the coordinates of C ?

(c) Write the equation of the line OC.

(a) OA = 6 ,OB =

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Qn 15.

In the figure A , B , C are the mid points of QR , PR , and PQ respectively.

A (2,4) R (5,5) B(4,7) .Then write the coordinates of P , Q , and C.

C (1, 6)

Q (-1,

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Qn 16.

The vertices of the parallelogram ABCD are A (-3 , 2) , B (1 , 5) ,C (4 , 9) Then

(a) Write the coordinates of D?

(b) Find the length of AB and AD

(c) Calculate the area of the parallelogram ?

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Qn 17.

In the figure ABCD is a parallelogram. Write the coordinates of point C

X coordinate of point C = 9 + 6 - 4 = 11

Y coordinate of point C = 8 + 6 - 2 =

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