Points A(-2,3), B(-5,-4), and C(2,-1) form triangle ABC on a coordinate plane. What is the area of this triangle in square units
?
2 answers:
1. Draw an accurate picture of the triangle in
the coordinate axes, as shown in the attached picture.<span>
<span>2. Circumscribe a rectangle about the triangle, as shown in
the picture. The coordinates of the points M, N, T are easily identifiable as shown in the
picture.</span>
<span>3. The area of the triangle ABC is The area of
the rectangle - Area 1- Area 2- Area 3.</span>
Area 1 = 1/2(3*7)=21/2
Area 2 = 1/2(4*4)=1/2*16=8
<span>Area 3 = 1/2( 3*7)=21/2</span>
<span>Area 1+Area 2+Area 3=21/2+21/2+8=21+8=29 (units squared)</span>
<span>Area rectangle= 7*7=49 (units squared)</span>
<span>Answer: Area of triangle is 20 units squared.</span></span>
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Answer:
Conjecture : 2xy / ( x + y ) ≤ √xy
Step-by-step explanation:
Harmonic mean of x and y = 2xy/( x + y )
<u>Formulate a conjecture about their relative sizes </u>
we will achieve this by computing harmonic and geometric means
Geometric mean = √xy
harmonic mean = 2xy/( x + y )
Conjecture : 2xy / ( x + y ) ≤ √xy
attached below is the proof
