Question

7. In each of the following, the co-ordinates of
the three vertices of a rectangle ABCD are
given. By plotting the given points; find, in
each case, the co-ordinates of the fourth
vertex :
(i) A (2, 0), B (8,0) and C (8, 4).​

Answer 1

Answer:

D (2,4) is the correct answer

Step-by-step explanation:

Let us assume

• (x, y)     = (2, 0)
• (x1, y1)  = (8, 0)
• (x2, y2) = (8, 4)`
• (x3, y3) = (?, ?)

When we join the diagonals of the rectangle i.e., AC and BD, we come to know that Mid-point of AC = Mid-point of BD.

∴ We shall apply the formula,

   [(x+x2)/2 , (y+y2)/2] = [(x1+x3)/2 , (y1+y3)/2]

⇒ [(2+8)/2 , (0+4)/2]    = [(8+x3)/2 , (0+y3)/2]

Now equating the like terms,

⇒ (2+8)/2 = (8+x3)/2         AND         (0+4)/2 = (0+y3)/2

⇒ 10 = 8+x3          AND          4 = 0+y3

⇒ ∴ x3 = 2          AND          y3 = 4

∴ D (x3, y3) = (2,4)            ←ANSWER  

                             OR

You can simply do it in your brain

If A=(2,0)   B=(8,0)      C=(8,4),

It means that point D will be above A and 'x' value will be 2 because it's a rectangle and 'y' value will be 4 because in the rectangle AB || CD and also because AD = BC i.e., AD = 4                    

PLEASE MARK AS THE BRAINLIEST!!!!!