Mr. Bernard needs to order boxes for his 18-inch diameter "Super Pizza."
1 answer:
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Answer:
The orthocentre of the given vertices ( 2 , -3.5)
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
The orthocentre is the intersecting point for all the altitudes of the triangle.
The point where the altitudes of a triangle meet is known as the orthocentre.
Given Points are K (3.-3), L (2,1), M (4,-3)
<em>The Altitudes are perpendicular line from one side of the triangle to the opposite vertex</em>
<em>The altitudes are MN , KO , LP</em>
<u><em>step(ii):-</em></u>
<em> </em> Slope of the line
The slope of MN =
The perpendicular slope of KL
=
The equation of the altitude
4y +12 = x -4
x - 4 y -16 = 0 ...(i)
Step(iii):-
Slope of the line
The slope of KO =
The perpendicular slope of LM
=
The equation of the altitude
The equation of the line passing through the point K ( 3,-3) and slope
m = 1/2
2y +6 = x -3
x - 2y -9 =0 ....(ii)
Solving equation (i) and (ii) , we get
subtracting equation (i) and (ii) , we get
x - 4y -16 -( x-2y-9) =0
- 2y -7 =0
-2y = 7
y = - 3.5
Substitute y = -3.5 in equation x -4y-16=0
x - 4( -3.5) - 16 =0
x +14-16 =0
x -2 =0
x = 2
The orthocentre of the given vertices ( 2 , -3.5)