Q) Reena has a 10 m × 10 m kitchen garden attached to her kitchen. She divides it into a 10 × 10 grid and wants to grow some vegetables and herbs used in the kitchen. She puts some soil and manure in that and sow a green chilly plant at A, a coriander plant at B and a tomato plant at C. Her friend Kavita visited the garden and praised the plants grown there. She pointed out that they seem to be in a straight line. See the below diagram carefully:

i. Find the distance between A and B.
ii. Find the mid-point of the distance AB.
iii. Find the distance between B and C.
iv. Find the mid point of BC.

Ans:

1. Distance between A and B:

Step 1: From the diagram, Coordinates of point A: (2, 2)

Coordinates of point B: (5, 4)

Step 2: We know that the distance between two points P (X₁, Y₁) and Q (X₂, Y₂) is given by:

PQ =

∴ Distance AB =

∴ AB =

∴ AB =

Therefore, the distance between points A and B is √13 m.

2. Mid point of AB:

Step 3: Now we have coordinates of point A (2, 2) and Point B (5, 4)

∵ We know that the coordinates of midpoint of 2 coordinates (X₁, Y₁) and (X₂, Y₂) given by:

(X, Y) =

∴ Coordinates of midpoint of A (2, 2) and B (5, 4) =

=

Therefore, the coordinates of midpoint of AB are (, 3).

3. Distance between B and C:

Step 4: From the diagram, Coordinates of point B: (5, 4)

Coordinates of point C: (7, 6)

Step 5: By putting values in distance formula (explained in step 2), we get:

∴ Distance BC =

∴ AB =

∴ AB =

Therefore, the distance between points A and B is 2 √2 m.

4. Mid point of BC:

Step 3: Now we have coordinates of point B (5, 4) and Point C (7, 6)

By putting values in distance formula (explained in step 3), we get:

Coordinates of midpoint of B (5, 4) and C (7, 6) =

= = (6, 5)

Therefore, the coordinates of midpoint of AB are (6, 5).

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