PLEASE ANSWER ASAP *picture attached*
1 answer:
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Nice. We're not really told which is the right angle. We can tell from the squared distances:
We see so B is the right angle.
That was preliminary and probably indicated in an associated figure.
Now we want the line through the midpoint of the legs, AB and BC, in standard form.
The midpoint of AB is the average of the coordinates of A and B:
The midpoint of BC is
The line through those points is
That's the answer. Let's check it.
Midpoint of AB is (-2,3), -2 + 8(3)=22 good.
Midpoint of BC is (2,5/2), 2+8(5/2)=22 good.
We know that
<span>the standard form equation of the circle is
(x-h)</span>²+(y-k)²=r²
where
(h,k)------> is the center
and
r----> is the radius
let
A------> the point <span>(−8, 0)
</span>B-------> the point <span>(−12, 2)
</span>
step 1
find the distance point A and point B
d=√[(2-0)²+(-12+8)²]------> d=√20-----> d=2√5 units
the distance AB is equals to the diameter
and
the radius r=2√5/2-----> r=√5 units
step 2 find the midpoint AB
midpoint ABx=(-8-12)/2-----> -10
midpoint ABy=(2+0)/2-----> 1
the midpoint is (-10,1)
the center is equal to the midpoint
so
(h,k)------> (-10,1)
step 3
find the equation of a circle
(x-h)²+(y-k)²=r²------> (x+10)²+(y-1)²=(√5)²
(x+10)²+(y-1)²=5
the answer is
(x+10)²+(y-1)²=5
see the attached figure
<span>the standard form equation of the circle is
(x-h)</span>²+(y-k)²=r²
where
(h,k)------> is the center
and
r----> is the radius
let
A------> the point <span>(−8, 0)
</span>B-------> the point <span>(−12, 2)
</span>
step 1
find the distance point A and point B
d=√[(2-0)²+(-12+8)²]------> d=√20-----> d=2√5 units
the distance AB is equals to the diameter
and
the radius r=2√5/2-----> r=√5 units
step 2 find the midpoint AB
midpoint ABx=(-8-12)/2-----> -10
midpoint ABy=(2+0)/2-----> 1
the midpoint is (-10,1)
the center is equal to the midpoint
so
(h,k)------> (-10,1)
step 3
find the equation of a circle
(x-h)²+(y-k)²=r²------> (x+10)²+(y-1)²=(√5)²
(x+10)²+(y-1)²=5
the answer is
(x+10)²+(y-1)²=5
see the attached figure