Math, asked by shweta1552003, 10 months ago

4. Three vertices of rectangle are A(2,2), B(2,-2) and C(-3,-2). Plot the points then find the co-
ordinates of he missing vertex.​

Answers

Answered by mysticd
17

 Given \: three \: Vertices \: of \: triangle \:are

 A(2,2),B(2,-2) \:and \: C(-3,-2)

 Let \: Fourth \:vertex \: D(x,y)

 Mid \: point \:of \: diagonal \:BD =

 Mid \:point \:of \: diagonal \: AC

 \implies \Big(\frac{x+2}{2} , \frac{y-2}{2}\Big) = \Big(\frac{2-3}{2} , \frac{2-2}{2}\Big)

 \implies \Big(\frac{x+2}{2} , \frac{y-2}{2}\Big) = \Big(\frac{-1}{2} , 0\Big)

 \frac{x+2}{2} = \frac{-1}{2} \:and \: \frac{y-2}{2}=0

 \implies x + 2 = - 1 \:and \: y -2 = 0

 \implies x  = - 1 - 2 \:and \: y  = 2

 \implies x  = - 3 \:and \: y  = 2

Therefore.,

 \red{ Fourth \:vertex (D) } \green { = ( -3,2)}

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Answered by Anonymous
1

Answer:

Given:

  • Three vertices of rectangle are A(2,2), B(2,-2) and C(-3,-2).

Find:

  • Plot the points then find the co-ordinates of he missing vertex.

Calculations:

  • Let "D" vertex be (x and y).

So,

⇢ x + 2/2 and x + 3/2

⇢ 2 - 3/2 and 2 - 2/2

⇢ x + 2/2 and y - 2/2 = -1/2 and 0.

⇢ x + 2 = -1

⇢ y - 2 = 0

⇢ x = -1 - 2

⇢ y = 2

Therefore, -3 and 2 is the fourth vertex of D.

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