a Use a ruler to draw a kite. Remember that in kites the diagonals are perpendicular.
B
b Draw four more kites using different values of x.
C
c Evaluate the perimeter of each kite and record them in a table.
D
d Use the table from the previous part to make a graph.
E
e If a kite has diagonals that bisect each other then it is a rhombus.
A
a See solution.
B
b See solution.
C
c See solution.
D
d See solution.
E
e See solution.
Practice makes perfect
a We are asked to redraw a kite with diagonals of 12 cm and 4 cm. To do this let's start with drawing a horizontal diagonal AC that has a length of 12 cm.
Next, as we want the point of intersection of the diagonals to be 2 cm from point A, we will draw a segment BD that is perpendicular to AC and satisfy this condition. Notice that we are given that the second diagonal has a length of 4 cm and in a kite one diagonal bisects the other.
Finally we can connect the vertices to form a kite ABCD.
b In this part we are asked to draw four more kites, but each time with different value of x. Let's choose x=4, 6, 8, and 10. We will name the vertices with consecutive letters.
c Now we will measure and record in a table the perimeter of each kite we draw, along with the x-value.
Kite
x
Perimeter
ABCD
2
≈ 26.1
EFGH
4
≈ 25.4
IJKL
6
≈ 25.3
MNOP
8
≈ 25.4
QRST
10
≈ 26.1
d In this part we will graph the perimeter versus the x-value using the data from the table we made in the previous part. Perimeter will be on the vertical axis and the x- values will be on the horizontal axis.
e Looking at the graph we made in Part D, we can assume that the perimeter will be minimized for x=6. It is a significant conclusion because for x=6 the diagonals bisect each other and the figure is a rhombus.
