Coordinate Geometry Test

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Coordinate Geometry Test - 20

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Question 1
1 / -0

If a point $$C$$ be the mid-point of a line segment $$AB$$, then $$AC = BC = (...) AB$$.

A
$$3$$

B
$$\dfrac{1}{2}$$

C
$$2$$

D
$$\dfrac{1}{4}$$

Solution

If $$C$$ is the midpoint of $$AB$$, then $$C$$ divides $$AB$$ in equal segments. Those segments are $$AC$$ and $$AB$$.
therefore, $$AC=BC$$.
$$AC+BC=AB$$ (As AC and BC are the segments of $$AB$$)
$$\Rightarrow 2AC=2BC=AB\\ \Rightarrow AC=BC=\dfrac{1}{2} AB$$
Question 2
1 / -0

Points $$(2,-3)$$, $$(-2,1)$$ are bisected at points :-

A
$$(6,-7)$$

B
$$(0,-1)$$

C
$$(-6,7)$$

D
$$(6,-5)$$

Solution
Question 3
1 / -0

Mid points of $$(1, 2)$$ and $$(3, 4)$$ is

A
$$(2, 3)$$

B
$$(3, 2)$$

C
$$(2, 4)$$

D
None of these

Solution

We have,

$$A\left( 1,2 \right),B\left( 3,4 \right)$$

We know that the mid-point formula,

$$\left( \dfrac{{{x}_{1}}+{{x}_{2}}}{2},\dfrac{{{y}_{1}}+{{y}_{2}}}{2} \right)$$

Therefore,

Mid-point

$$ =\left( \dfrac{1+3}{2},\dfrac{2+4}{2} \right) $$

$$ =\left( \dfrac{4}{2},\dfrac{6}{2} \right) $$

$$ =\left( 2,3 \right) $$

Hence, this is the answer.
Question 4
1 / -0

Find the mid point of $$(9,5)$$ and $$(3,7)$$

A
$$(6,6)$$

B
$$(12,12)$$

C
$$(2,2)$$

D
$$(1,1)$$

Solution

Given points $$(9,5),(3,7)$$
Midpoint formula
Midpoint is given as $$\left(\dfrac{x_1+x_2}2,\dfrac{y_1,y_2}{2}\right)\\\left(\dfrac{9+3}{2},\dfrac{5+7}{2}\right)\\\left(\dfrac{12}{2},\dfrac{12}{2}\right)=(6,6)$$
Question 5
1 / -0

If $$O(0,4)$$ and $$P(0,-4)$$, are the coordinates of the line segment $$OP$$ then co-ordinate of its midpoint is

A
$$(0,-4)$$

B
$$(0,4)$$

C
$$(-4,0)$$

D
$$(0,0)$$

Solution

Midpoint of a line segment having coordiantes $$\left({x}_{1},{y}_{1}\right)$$ and $$\left({x}_{2},{y}_{2}\right)$$ is $$\left(\dfrac{{x}_{1}+{x}_{2}}{2},\dfrac{{y}_{1}+{y}_{2}}{2}\right)$$
$$\therefore $$ Modpoint of $$OP=\left(\dfrac{0+0}{2},\dfrac{4+-4}{2}\right)$$
$$=\left(0,0\right)$$
Question 6
1 / -0

The mid point of $$(-1,-3)$$ and $$(3,7)$$ is

A
(1, 2)

B
(0, 2)

C
(0, 4)

D
(2 ,2)

Solution

Given points $$(-1,-3),(3,7)$$
Mid point is given as $$\left(\dfrac {-1+3}{2},\dfrac {-3+7}{2}\right)=(1,2)$$
Question 7
1 / -0

The mid points of three sides of a triangle are (0, 1) (0, 2) and (0, 3). Area of this triangle.

A
3

B
0

C
1

D
None of these

Solution
Question 8
1 / -0

The coordinates of the midpoint of a line segment joining $$P ( 5,7 )$$ and Q $$( - 3,3 )$$ are

A
$$(2,4 )$$

B
$$(1, 5) $$

C
$$(4,2)$$

D
$$(5,2)$$

Solution

Let two points $$\ (x_1, y_1)$$ and $$\ (x_2, y_2)$$ then midpoint of line joining these two points is given by $$\bigg(\dfrac{x_1+x_2}{2}, \dfrac{y_1 +y_2}{2}\bigg)$$
Given $$P(5,7)$$ and $$Q(-3,3)$$

Mid of $$PQ$$ will be $$\bigg(\dfrac{5-3}{2},\dfrac{7+3}{2}\bigg)$$
$$=\bigg(\dfrac{2}{2},\dfrac{10}{2}\bigg)=(1,5)$$
Question 9
1 / -0

A(3 , 2) and B(5 , 4) are the end points of a line segment . Find the coordinates of the mid-point of the line segment .

A
(1 , 3)

B
(2 , 3)

C
(3 , 2)

D
(4 , 3)

Solution

Given,

$$A(3,2),B(5,4)$$

Mid point of $$AB$$

$$=\left ( \dfrac{3+5}{2},\dfrac{2+4}{2} \right )$$

$$=(4,3)$$
Question 10
1 / -0

The mid point of $$(8,3)$$ and $$(4,9)$$ is

A
$$(6,6)$$

B
$$(4,4)$$

C
$$(9,9)$$

D
$$(2,2)$$

Solution

The given points are $$(8,3)$$ and $$(4,9)$$
The mid point is given as $$ \left(\dfrac {8+4}2,\dfrac {3+9}2\right)\\=(6,6)$$

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Re-Attempt Weekly Quiz Competition

Coordinate Geometry Test - 20

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Coordinate Geometry Test - 20

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SHARING IS CARING

Question 1

$$3$$

$$\dfrac{1}{2}$$

$$2$$

$$\dfrac{1}{4}$$

Solution

Question 2

$$(6,-7)$$

$$(0,-1)$$

$$(-6,7)$$

$$(6,-5)$$

Solution

Question 3

$$(2, 3)$$

$$(3, 2)$$

$$(2, 4)$$

None of these

Solution

Question 4

$$(6,6)$$

$$(12,12)$$

$$(2,2)$$

$$(1,1)$$

Solution

Question 5

$$(0,-4)$$

$$(0,4)$$

$$(-4,0)$$

$$(0,0)$$

Solution

Question 6

(1, 2)

(0, 2)

(0, 4)

(2 ,2)

Solution

Question 7

3

0

1

None of these

Solution

Question 8

$$(2,4 )$$

$$(1, 5) $$

$$(4,2)$$

$$(5,2)$$

Solution

Question 9

(1 , 3)

(2 , 3)

(3 , 2)

(4 , 3)

Solution

Question 10

$$(6,6)$$

$$(4,4)$$

$$(9,9)$$

$$(2,2)$$

Solution

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