Question

Krishna has an apple Orchard which has a 10m×10m sized kitchen garden attached to it. she divides it into a 10×10 grid and puts soil and manure into it. she grows a lemon plant at A,a coriander plant at B, an onion plant at C and a tomato plant at D. Her husband Ram planes her kitchen garden and praised her kitchen garden and points out that on joining A, B, C and D they may form a parallelogram. Answer the following question (i)write the coordinates of the points a b c and d using the 10 × 10 grid as coordinate Axes. (ii) find whether ABCD is a parallelogram or
not​

Answer 1

Krishna has an apple Orchard which has a 10m×10m sized kitchen garden attached to it. she divides it into a 10×10 grid and puts soil and manure into it.

From given figure, we have,

A (2, 2) B (5, 4) C (7, 7) D (4, 5)

Now, we need to find the slopes of lines formed by these points.

Therefore, we use the formula,

Slope = y₂ - y₁ / x₂ - x₁

Slope of line AB = A (2, 2) B (5, 4)

= 4 - 2 / 5 - 2

= 2 / 3

Slope of line BC = B (5, 4) C (7, 7)

= 7 - 4 / 7 - 5

= 3 / 2

Slope of line CD = C (7, 7) D (4, 5)

= 5 - 7 / 4 - 7

= -2 / -3 = 2 / 3

Slope of line DA = D (4, 5) A (2, 2)

= 2 - 5 / 2 - 4

= -3 / -2 = 3 / 2

Slop of AB = Slope of CD

⇒ AB ║ CD

Slope of BC = Slope of DA

⇒ BC ║ DA

Now to find the distance between the points, we use distance formula, given by,

d = √ (x₂ - x₁)² + (y₂ - y₁)²

AB = √ (5 - 2)² + (4 - 2)²  = √ ( 9 + 4  ) = √ 13

BC = √ (7 - 5)² + (7 - 4)² = √ ( 4 + 9  ) = √ 13

CD = √ (4 - 7)² + (5 - 7)² = √ ( 9 + 4  ) = √ 13

DA = √ (4 - 2)² + (5 - 2)² = √ ( 4 + 9  ) = √ 13

AB = BC = CD = DA = √ 13

ABCD is a parallelogram.