What is the area of a triangle with vertices at (0,-2),(8,-2), and (9,1)
2 answers:
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we will proceed to resolve each case to determine the solution
we have
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
<u>case a)</u>
Substitute the value of x and y in the inequality
-------> is true
so
The ordered pair is a solution
<u>case b)</u>
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
<u>case c)</u>
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
<u>case d)</u>
Substitute the value of x and y in the inequality
-------> is True
so
The ordered pair is a solution
<u>case e)</u>
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
Verify
using a graphing tool
see the attached figure
the solution is the shaded area below the line
The points A and D lies on the shaded area, therefore the ordered pairs A and D are solution of the inequality
Answer:
A non-equilateral rhombus.
Step-by-step explanation:
We can solve this graphically.
We start with square:
ABCD
with:
A = (11, - 7)
B = (9, - 4)
C = (11, - 1)
D = (13, - 4)
Only with the vertices, we can see that ABCD is equilateral, as the length of each side is:
AB = √( (11 - 9)^2 + (-7 -(-4))^2) = √( (2)^2 + (3)^2) = √(4 + 9) = √13
BC = √( (11 - 9)^2 + (-1 -(-4))^2) = √13
CD = √( (11 - 13)^2 + (-1 -(-4))^2) = √13
DA = √( (11 - 13)^2 + (-7 -(-4))^2) = √13
And we change C by C' = (11, 1)
In the image you can see the 5 points and the figure that they make:
The figure ABCD is a rhombus, and ABC'D is also a rhombus, the only difference between the figures is that ABCD is equilateral while ABC'D is not equilateral.
