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Nostrana [21]
3 years ago
10

14. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5). Show your work.

Mathematics
2 answers:
kap26 [50]3 years ago
8 0

Answer:4.5,-1


Step-by-step explanation:

YM=(8+1)/2→XM=45

YM=(-5+3)/3→YM=-1

The midpoint is (4.5,-1)


Stells [14]3 years ago
7 0
As in the solution of all geometry problems, the first step is to draw a diagram.  In this case, we see a right-triangle for which finding the circumcentre is almost trivial.

Recall that the circumcentre is the centre of a circle which passes through all three points D, E and F (shown as A,B & C in the attached figure).

The circumcentre can be found by the intersection of the perpendicular bisectors of the three sides.  Since the three bisectors are concurrent, we only need the intersection of any two perpendicular bisectors out of the three.

In a right triangle where the legs are parallel to the axes, the intersection of the perpendicular bisectors can be found by inspection.

In the given case, 
mid-point of DE (shown as AB) = ((1+8)/2, 3) = (4.5,3)
   perpendicular bisector of DE :  x=4.5
mid-point of DF (shown as AC) = (1, (3-5)/2) = (1,-1)
   perpendicular bisector of DF :  y=-1

Therefore the circumcentre is the intersection of x=4.5 and y=-1, or
   circumcentre = (4.5,-1)

which brings us to the interesting property of the circumcentre of a right-triangle:  The circumcentre of a right triangle is located at the mid-point of the hypotenuse.

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Simplifying Complex fractions using any method
zloy xaker [14]

Answer:

3ab

-------------------

(b+a)

Step-by-step explanation:

3/a - 3/b

-------------------

1/a^2 - 1/b^2

Multiply the top and bottom by a^2 b^2/ a^2/b^2 to clear the fractions

(3/a - 3/b) a^2 b^2

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(1/a^2 - 1/b^2) a^2b^2

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Factor out 3ab on the top

3ab( b-a)

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b^2 -  a^2

The bottom is the difference of squares

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6 0
3 years ago
Read 2 more answers
Help!!!!!!!!!!!!!!!!!!!!
lapo4ka [179]
Well...   the segment FG = 4x + 3, the segment GH = 7x - 12, now, the
 
segment FH = FG + GH, those two fellows added up, and we know that FG and GH are both equal halves because G is the midpoint.

thus, FG = GH
or

\bf 4x+3=7x-12\implies 3+12=7x-4x\implies 15=3x
\\\\\\
\cfrac{15}{3}=x\implies \boxed{5=x}\\\\
-------------------------------\\\\
thus\qquad 
\begin{cases}
\overline{FG}=4x+3\\
4(5)+3\\
23\\
------\\
\overline{GH}=7x-12\\
7(5)-12\\
23
\end{cases}\impliedby equal\ halves
\\\\\\
\overline{FH}=23+23\implies \overline{FH}=46\implies 6y-2=46
\\\\\\
6y=46+2\implies y=\cfrac{48}{6}

and fairly sure, you know how much that is.
7 0
3 years ago
Help me pls
expeople1 [14]

I think you can find it graphically by points through a table you create like:

let x = 0, and find the value of y

for example for the first equation when we let x = 0 you find y = 6 and be in the form of (0,6) then draw them or you can let x = -2 or -3 , etc as you like

to be more accurate you can find 3 pionts and start graphing them

these two equations are straight lines and they will intersect in a point

5 0
2 years ago
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