Question

The diagonals of a rhombus intersect at the point (0,4). If one endpoint of the longer diagonal is located at point (4,10))

What is other ended point??

Answer 1

$\large{\green{\bf{Answer}}}$

The other endpoint is located at (-4,-2)

Explanation

• The diagonals of a rhombus bisect each other.

• The diagonals of a rhombus intersect at the midpoint of each diagonal.

• Hence, The point (0,4) is the midpoint of the two diagonals.

Answer 2

Answer:

$\bold\red{(-4,-2)}$

Step-by-step explanation:

Let the other end point of the diagonal be (x,y)

Now,

It is given that,

Diagonals are interesting each other at (0,4)

But, we know that,

Diagonals of a rhombus bisects each other.

So, according to this,

(0,4) is the mid point of the diagonal.

Also,

(4,10) is first end point of the diagonal.

we know that,

If (a,b) and (c,d) are two ends of a line segment,

then it's mid point (m,n) is given by,

$\bold\green{(m,n)=(\frac{a+c}{2},\frac{b+d}{2})}$

So,

According to this,

we get,

$(0,4)=(\frac{4+x}{2},\frac{10+y}{2})$

Comparing, we get,

$\frac{4 + x}{2} = 0 \\ \\ = > 4 + x = 0 \\ \\ = > x = - 4$

and,

$\frac{10 + y}{2} = 4 \\ \\ = > 10 + y = 8 \\ \\ = > y = - 2$

Therefore we got the point

( x , y ) = ( -4 , -2 )

Hence,

the other point of the diagonal is (-4,-2)