Question

the three vertices of a square abcd are a(5,4) b(6,9) and c(11,8) . what are the coordinates of the vertext d

Answer 1

Answer:

★Question★

• The three vertices of a square ABCD are A(5,4) B(6,9) and C(11,8). What are the coordinates of the vertex D?

★Answer★

Given ::-

• The three vertices of a square ABCD are A(5,4) B(6,9) and C(11,8)

To find :-

• The coordinates of the vertex D

Property Used :-

• Diagonals of a square bisect each other.

Formula used:-

• Suppose the endpoints of the line are P(x1, y2) and Q(x2, y2) then the midpoint R(x, y) is calculated using the formula given below.

The Midpoint Formula is given as,

$\bf\implies \:( x,y ) = (\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} )$

Solution :-

The three vertices of a square ABCD are A(5,4) B(6,9) and C(11,8)

Let the coordinates of D be (x, y).

Since, in square, diagonal bisects each other.

$\longmapsto\tt\boxed{Midpoint \: of \: AC = Midpoint \: of \: BD}$

Using Midpoint Formula, we get

$\bf\implies \:(\dfrac{5 + 11}{2} ,\dfrac{4 + 8}{2} ) = ( \dfrac{6 + x}{2} , \dfrac{9 + y}{2} )$

So, on comparing, we get

$\bf\implies \:16 = 6 + x \: and \: 12 = 9 + y$

$\bf\implies \:x = 10 \: and \: y = 3$

$\bf\implies \:The \: coordinates \: of \: vertex \: D \: is \: (10 , 3)$

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