Coordinate Geometry Test

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Coordinate Geometry Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

The centroid and two vertices of a triangles are (4,-8), (-9,7), (1,4) then the area of the triangle is

A
333 sq.units

B
166.5 sq.units

C
111 sq.units

D
55.5 sq.units
Question 2
1 / -0

The centre of a circle passing through the points (0 , 0), (1 , 0) and touching the circle $$x^2 + y^2$$ = 9

A
($$\frac{3}{2} , \frac{1}{2}$$)

B
($$\frac{1}{2} , \frac{3}{2}$$)

C
($$\frac{1}{2} , \frac{1}{2}$$)

D
($$\frac{1}{2} , -2 \dfrac{1}{2}$$)
Question 3
1 / -0

A circle passes through point $$\left( 3 , \sqrt { \frac { 7 } { 2 } } \right)$$ touches the line pair $$x ^ { 2 } - y ^ { 2 } - 2 x + 1 = 0$$. Center of the circle lies inside the circle $$x ^ { 2 } + y ^ { 2 } - 8 x + 10 y + 15 = 0 .$$ Co-ordinate of centre of circle is

A
$$( 4,0 )$$

B
$$( 5,0 )$$

C
$$( 6,0 )$$

D
$$( 0,4 )$$

Solution
Question 4
1 / -0

The centers of the passing through (0,0) and (1,0) and touching the circle $${ x }^{ 2 }+{ y }^{ 2 }=9$$is

A
$$\left( \dfrac { 1 }{ 2 } ,\dfrac { 1 }{ 2 } \right) $$

B
$$\left( \dfrac { 1 }{ 2 } -\sqrt { 2 } \right) $$

C
$$\left( \dfrac { 3 }{ 2 } ,\dfrac { 3 }{ 2 } \right) $$

D
$$\left[ \dfrac { 1 }{ 2 } ,\dfrac { 3 }{ 2 } \right] $$
Question 5
1 / -0

In $$\triangle ABC,A(1,2);B(5,5),\angle ACB={ 90 }^{ 0 }$$. If area of $$\triangle ABC$$ is to be 6.5 sq. units, then the possible number of points for C is

A
1

B
2

C
0

D
4
Question 6
1 / -0

A line forms a triangle of area $$54\sqrt { 3 } $$ sq-units with the coordinate axes. Then the equation of the line if the perpendicular drawn from the origin to the line makes an angle of $${ 60 }^{ \circ }$$ with the x-axis is

A
$$x-\sqrt { 3 } y=18$$

B
$$x+\sqrt { 3 } y=18$$

C
$$x+\sqrt { 3 } y=-18$$

D
None of these

Solution
Question 7
1 / -0

If the area of the triangle formed by the line -y = 0, x + y = 0 and x - c = 0 is 16 units, c is

A
1

B
2

C
4

D
8
Question 8
1 / -0

Let $$A(h,k),B(1,1)$$ and $$C(2,1)$$ be the vertices of a right- angled triangle with $$AC$$ as its hypotenuse. If the area of the triangle is 1, then the set of values which $$k$$ can take is given by

A
{1, 3}

B
{0, 2}

C
{-1, 3}

D
{-3, 2}

Solution
Question 9
1 / -0

If the tangent at (3,-4) to the circle $${ x }^{ 2 }+{ y }^{ 2 }-4x+2y-5=0$$ cuts the circle $${ x }^{ 2 }+{ y }^{ 2 }-16x+2y+10=0$$ in A and B then the midpoint of AB is

A
(-6,-7)

B
2,-1)

C
(2, 1)

D
(5, 4)
Question 10
1 / -0

If the distance of given point $$\left( \alpha ,\beta \right) $$ from each of two straight lines through the origin is d, then the value of $$\left( \alpha y-\beta x \right) ^{ 2 }$$ is equal to

A
$${ d }^{ 2 }({ x }^{ 2 }-{ y }^{ 2 })$$

B
$${ d }^{ 2 }({ x }^{ 2 }+{ y }^{ 2 })$$

C
$${ d }^{ 2 }({ x }+{ y })$$

D
None of these

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Re-Attempt Weekly Quiz Competition

Coordinate Geometry Test - 51

Result

Coordinate Geometry Test - 51

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Rank

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SHARING IS CARING

Question 1

333 sq.units

166.5 sq.units

111 sq.units

55.5 sq.units

Question 2

($$\frac{3}{2} , \frac{1}{2}$$)

($$\frac{1}{2} , \frac{3}{2}$$)

($$\frac{1}{2} , \frac{1}{2}$$)

($$\frac{1}{2} , -2 \dfrac{1}{2}$$)

Question 3

$$( 4,0 )$$

$$( 5,0 )$$

$$( 6,0 )$$

$$( 0,4 )$$

Solution

Question 4

$$\left( \dfrac { 1 }{ 2 } ,\dfrac { 1 }{ 2 } \right) $$

$$\left( \dfrac { 1 }{ 2 } -\sqrt { 2 } \right) $$

$$\left( \dfrac { 3 }{ 2 } ,\dfrac { 3 }{ 2 } \right) $$

$$\left[ \dfrac { 1 }{ 2 } ,\dfrac { 3 }{ 2 } \right] $$

Question 5

1

2

0

4

Question 6

$$x-\sqrt { 3 } y=18$$

$$x+\sqrt { 3 } y=18$$

$$x+\sqrt { 3 } y=-18$$

None of these

Solution

Question 7

1

2

4

8

Question 8

{1, 3}

{0, 2}

{-1, 3}

{-3, 2}

Solution

Question 9

(-6,-7)

2,-1)

(2, 1)

(5, 4)

Question 10

$${ d }^{ 2 }({ x }^{ 2 }-{ y }^{ 2 })$$

$${ d }^{ 2 }({ x }^{ 2 }+{ y }^{ 2 })$$

$${ d }^{ 2 }({ x }+{ y })$$

None of these

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