Question

please answer these questions​

Answer 1

✮ Answer:

B) Parallelogram

❒ Concept used:

• A figure is said to be a Parallelogram when the opposite sides are parallel to each other.
• A figure is said to be a trapezium when only 1 pair of opposite sides are parallel and the other pair is not parallel.

❃ Explanation:

➝ Refer the graph* which is plotted for the given points in the attachment.

➝ When an imaginary line is drawn passing through the points, we can observe that opposite sides are parallel.

∴ The given coordinates form a Parallelogram.

*Graph attached is made with Desmos graph

Answer 2

$\sf\huge\bold{Answer:}$

Given :

Points :

• P(-2,1)
• Q(2,1)
• R(3,2)
• S(-1,2)

To find :

• Plotting the points P, Q, R,S
• Whether the figure is a trapezium or parallelogram.

Solution :

Using distance formula :

$\boxed{\tt \red{d = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } } }$

where $\tt x_1$ and $\tt x_2$ are x coordinates of 1st and 2nd point respectively

and $\tt y_1$ and $\tt y_2$ are y coordinates of 1st and 2nd point respectively

To find PQ

• P(-2,1)
• Q(2,1)

PQ = √ [2-(-2)]²+(1-1)²

PQ = √ (2+2)²+(0)²

PQ = √(4)²+0

PQ = √16

PQ = 4units

To find QR

• Q(2,1)
• R(3,2)

QR = √ (3-2)²+(2-1)²

QR = √ (1)²+(1)²

QR = √1+1

QR = √2units

To find RS

• R(3,2)
• S(-1,2)

RS = √ (-1-3)²+(2-2)²

RS = √(-4)²+(0)²

RS = √ 16+0

RS = √16

RS = 4units

To find SP

• S(-1,2)
• P(-2,1)

SP = √[-2-(-1)]²+(1-2)²

SP = √[-2+1]²+(-1)²

SP = √(-1)²+1

SP = √1+1

SP = √2 units

Hence,

PQ=RS

QR=SP

Since,

Opposite sides of a quadrilateral are equal, it forms a parallelogram.$\:\:\:\:$ [trapezium does not have equal opposite sides]

PQRS forms a Parallelogram.