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**Q.1. AOBC is a rectangle whose three vertices are A (0, 3), O (0, 0) and B (5, 0). Find the length of its diagonal.Ans.** Length of diagonal = AB =

Ans.

∴

[ΔPQR is replaced by ΔDEF]

Ans.

∴

⇒

Ans.

∴ Area of ΔABC = 0

⇒

⇒

⇒

⇒

⇒

Ans.

According to the question,

PA = QA

On squaring both sides, we get

y

y

⇒ y(y + 5) + 3(y + 5) = 0

⇒ (y+ 5) (y + 3) = 0

⇒ y + 5 = 0

⇒ y = -5

and y + 3 = 0

⇒ y = -3

∴ y = -3, -5

Now,

For y = -3

and for y = -5

Hence, values of y are - 3 and -5,

Ans.

Since we know that diagonals of a parallogram bisect each other.

So, mid-point of AC

Mid-point of BD

Mid-point of AC and BD are

By comparison

x = 7, y = 3

Coordinates of D are (7, 3).

and coordinates of E are

Area of ΔADE

(i) The-median from A meets BC at D. Find the coordinates of the point D.

(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.

(iii) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.

(iv) What are the coordinates of the centroid of the triangle ABC?

Ans.

(ii) If P is point on AD, then by section formula

(iii) Same

∴ Its centroid divides all the medians in the ratio 2 : 1

(iv) Coordinates of the centroid are

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