Question

please help me in this problems I need the answers if all of this questions please help​

Answer 1

1.

(i) In a rhombus the length of all sides will be equal.

(ii) Diagonals will bisect each other. So, its midpoint will be equal.

So now,

=> (-4+8/2 , -7+5/2) = (-1+5/2 , 2-4/2)

=> (4/2,-2/2) = (4/2,-2/2)

=> (2,-1) = (2,-1)

So diagonals bisect each other.

=> √(-1+4)² + (2+7)² = √9+81 = √100 = 10

=> √(8+1)² + (5-2)² = √81 + 9 = √100 = 10

=> √(5-8)² + (-4-5)² = √9+81 = √100 = 10

=> √(-4-5)² + (-7+4)² = √81+9 = √100 = 10

Thus all the sides are equal .

Therefore the given coordinates are vertices of a rhombus.

2.Let the point be (x,0).

=> √(2-x)²+(-5-0)² = √(-2-x)²+(9-0)²

=> (2-x)² + (-5-0)² = (-2-x)² + (9-0)²

=> 4+x²-8x+25 = 4+x²+4x+81

=> -8x-4x = 81-25

=> -12x = 56

=> x = -(56/12)

=> x = -(14/3)

Thus the point X is (-14/3,0)