We appreciate your visit to Triangle KLM has vertices at K 5 8 L 2 5 and M 7 4 What is the area in square units of triangle KLM. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Answer:
9 square units
Step-by-step explanation:
You want the area of triangle KLM with vertices K(-5, -8), L(-2, -5), and M(-7, -4).
Pick's theorem
For small polygons with vertices on the coordinate grid, the area is conveniently found using the formula ...
A = i + b/2 -1
where i is the number of interior grid points, and b is the number of boundary grid points.
Application
In the attached, we have identified the interior grid points in red. There are 7 of them. The boundary grid points are blue, and there are 6 of them. That means the area is ...
A = 7 +(6/2) -1 = 9
The area of the triangle is 9 square units.
__
Additional comment
The area was also found using the geometry program that drew the triangle. It found the area to be 9 square units.
The area can be found directly from the grid point coordinates as half the absolute value of the sum of determinants of pairs of points.
A = 1/2|((-2)(-4)-(-5)(-7) +(-7)(-8) -(-4)(-5) +(-5)(-5) +(-8)(-2)|
A = 1/2|8 -35 +56 -20 +25 -16| = 1/2|18| = 9 . . . . square units
And, the area can be found from the graph by subtracting the three corner triangle areas from the bounding rectangle area.
A = 5×4 -1/2(5×1 +3×3 +2×4) = 20 -1/2(5 +9 +8) = 9 . . . . square units
The determinant of a pair of points, as used above, is ...
[tex]\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-cb[/tex]
It does not matter whether the point coordinates are written as a row, or as a column. The determinant is the same in either case. What matters is that the points are used in the same order. Above, we used LM, MK, KL as the pairs of points.
<95141404393>
Thanks for taking the time to read Triangle KLM has vertices at K 5 8 L 2 5 and M 7 4 What is the area in square units of triangle KLM. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Step-by-step explanation:
K(-5;-8) L(-2;-5) M(-7;-4) SΔKLM=?
The area of a KLM triangle with vertices at points A(x₁;y₁), B(x₂;y₂), C(x₃;y₃) can be calculated using the formula:
[tex]\displaystyle\\S_{KLM}=\frac{1}{2} *|(x_2-x_1)*(y_3-y_1)-(x_3-x_1)*(y_2-y_1)|[/tex]
[tex]x_1=-5\ \ \ \ \ \ x_2=-2\ \ \ \ \ \ x_3=-7\ \ \ \ \ \ y_1=-8\ \ \ \ \ \ y_2=-5\ \ \ \ \ \ y_3=-4[/tex]
[tex]\displaystyle\\S _{KLM}=\frac{1}{2}*|(-2-(-5))*(-4-(-8))-(-7-(-5))*(-5-(-8))|\\\\\\S_{KLM}=\frac{1}{2}*|(-2+5)*(-4+8)-(-7+5)*(-5+8)|\\\\\\S_{KLM}=\frac{1}{2} *|3*4-((-2)*3|\\\\\\S_{KLM}=\frac{1}{2}*|12+6|\\\\\\S_{KLM}=\frac{1}{2} *|18|\\\\\\S_{KLM}=\frac{18}{2} \\\\\\S_{KLM}=9 \ square\ units.[/tex]
[tex]Answer: \ S_{KLM}=9 \ square\ units.[/tex]
