Question

Three vertices of a square are A(-1, -9), B(3, -1) and C(-5, 3). Plot the points. Then find the coordinates of the missing vertex D​

Answer 1

Given :- Three vertices of a square are A(-1, -9), B(3, -1) and C(-5, 3) .

To Find :- find the coordinates of the missing vertex D ?

Concept and formula used :-

• Diagonals of a square are equal in length and bisect each other.
• Mid - Point formula :- if (x,y) is equidistant from (x1,y1) and (x2,y2) than, x = (x1 + x2)/2 and y = (y1 + y2)/2 .

Solution :-

Given that, A(-1, -9), B(3, -1) and C(-5, 3) .

Let coordinates of D are (x,y).

So,

we told above in square , diagonals are same and bisect each other.

Using mid - point formula we get,

→ mid point of AC = mid point of BD

Putting values we get,

→ {(-1 - 5)/2 , (-9 + 3)/2} = {(3 + x)/2 , (-1 + y)/2}

→ (-3, -3) = {(3 + x)/2 , (-1 + y)/2}

Comparing both we get,

→ (3 + x)/2 = (-3)

→ 3 + x = 2 * (-3)

→ 3 + x = (-6)

→ x = (-6) - 3

→ x = (-9) .

and,

→ (-1 + y)/ 2 = (-3)

→ (-1 + y) = 2 * (-3)

→ y - 1 = (-6)

→ y = (-6) + 1

→ y = (-5)

Hence, coordinates of the missing vertex D are {(-9) , (-5)}.