Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).
<h3>What are Diagonals of a Parallelogram?</h3>The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: .
A diagonal is XZ.
X(2, 5) = (x1, y1)
Z(0, 0) = (x2, y2)
Plug in the values
= (1, 2.5).
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Answer:
Step-by-step explanation:
The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.
Vertices A, B, and C form a right triangle with legs ,
, and
. The two legs, 3 and 4, represent the triangle's height and base, respectively.
The area of a triangle with base and height
is given by
. Therefore, the area of this right triangle is:
The other triangle is a bit trickier. Triangle is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:
, where
,
, and
are three sides of the triangle and
is the semi-perimeter (
).
The semi-perimeter, , is:
Therefore, the area of the isosceles triangle is:
Thus, the area of the quadrilateral is: