The two opposite vertices of a square as shown in the figure are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
B= (1, 0) and D= (1, 4)
O is the point of intersection of AC and BD so O is the midpoint of AC. AC is parallel to X-axis since its y-coordinates are constant.
∴ AC= ∣∣difference of x coordinates of A and C∣∣
=∣∣−1−3∣∣
= 4
∴ AO = AC2
= 2
Let coordinates of 'O' be (x,2)
⇒ {x coordinate of O} - {x coordinate of A} = 2 (∵ AO = 2)
⇒ (x-(-1)) = 2
⇒x=1
∴ O = (1,2)
∵ Diagonals of square are perpendicular to each other so BD will be parallel to Y-axis.
Now AO = BO (∵ diagonals of a square are equal and bisect each other)
∴ BO = 2
Let B = x1,y1
⇒ {y coordinate of O} - {y coordinate of B} = 2
⇒2−y1=2
⇒y1=0
and {x-coordinate of B} = {x-coordinate of O}
∴x1=1
∴ B = (1, 0)
and ⇒ {y coordinate of D} - {y coordinate of B} = 4 (∵ BD = 4)
⇒ y coordinate of D - 0 = 4
⇒ y coordinate of D = 4
∴ D = (1,4)
∵x−coordinate of D=x−coordinate of B)