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), where is the other endpoint located?​

Answer 1

Solution

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:-

(-4,-2)

Explanation:-

Given:-

Diagonals of rhombus intersect at a point (0,4).

One end point of the longer diagonal is (4,10)

To Find:-

Another end point

Solution:-

w.k.t,

• diagonals of rhombus bisect each other.
• Hence, the given point is a Midpoint.

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

From Midpoint formula

$\boxed{\bold{Midpoint(M) =[ \dfrac{x_1+x_2}{2} , \: \dfrac{y_1 +y_2}{2}]}}$

$(0,4) =[ \dfrac{x + 4}{2} , \: \dfrac{y +10}{2}]$

Equate abcissa and ordinate

$\dfrac{x + 4}{2} = 0$

$x + 4 = 0$

$\bold{ x = -4}$

Now,

$\dfrac{y + 10}{2} = 4$

$y +10 = 8$

$y = 8 - 10$

$\bold{y = -2}$

Hence, the point is

(-4,-2)