Question

In a parallelogram, the ends of one diagonal
are (3, -4) and (2, 3). If the second
diagonal has one end at (6, -1) then its
other end is​

Answer 1

The other end of second diagonal is (-1, 0).

In a parallelogram, the ends of one diagonal are (3, -4) and (2,3).

If the second diagonal has one end at (6, -1) then we have to find its other end.

For parallelogram,

“Midpoint of each diagonal must be the same point.”

means,

Midpoint of first diagonal = midpoint of second diagonal

Here,

ends of one diagonal are (3, -4) and (2, 3) and second diagonal has one end (6, -1).

let other end of second diagonal is (x, y).

⇒midpoint of (3, -4) and (2, 3) = midpoint of (6, -1) and (x , y)

⇒[ (3 + 2)/2 , (-4 + 3)/2 ] = [ (6 + x)/2 , (-1 + y)/2 ]

⇒[5/2 , -1/2 ] = [(6 + x)/2, (-1 + y)/2 ]

∴ (6 + x)/2 = 5/2 ⇒x = -1

and (-1 + y)/2 = -1/2 ⇒y = 0

Therefore the other end of second diagonal is (-1, 0).