Question

question 5 (2 points)

the coordinates of the vertices of rhombus abcd are a(1, 1), b(5, 3), c(7, 7), and d(3, 5).

what are the coordinates of the point of intersection of the diagonals? type the correct answers in the blanks.

x =

y =

Explanation:

Identify the diagonals of the rhombus

The vertices of the rhombus are given in order as \(A(1, 1)\), \(B(5, 3)\), \(C(7, 7)\), and \(D(3, 5)\).
The diagonals of rhombus \(ABCD\) connect opposite vertices, which are \(AC\) and \(BD\).

Apply the midpoint property of diagonals

The diagonals of a rhombus bisect each other.
Therefore, their point of intersection is the midpoint of either diagonal \(AC\) or \(BD\).

Calculate the coordinates of the midpoint

Using the midpoint formula on diagonal \(AC\) with \(A(1, 1)\) and \(C(7, 7)\):

$$ x = \frac{1 + 7}{2} = 4 $$

$$ y = \frac{1 + 7}{2} = 4 $$

Answer:

The coordinates of the vertices of rhombus ABCD are A(1, 1), B(5, 3), C(7, 7), and D(3, 5).

What are the coordinates of the point of intersection of the diagonals? Type the correct answers in the blanks.

x = <blank>4</blank>

y = <blank>4</blank>