The circumcenter is the center of the circle which goes through the triangle's vertices, so the circumcenter of the triangle and the center of that circumscribed circle MUST be the same point.
The same goes for the incenter and the center of the inscribed circle, though these will not, in general, be the same point as the circumcenter.
Perpendicular lines have slopes that multiply to get -1
y=mx+b is the slope intercept equation
m=slope
so get into y=mx+b form
-x+2y=4
solve for y
add x both sides
2y=x+4
divide by 2 both sides
y=(1/2)x+2
the slope is 1/2
perppendicular line slope multiplies to -1
1/2 times what=-1
times 2/1 both sides
what=-2/1=-2
y=-2x+b
find b
we are given a point is (-2,1)
when x=-2, y=1
1=-2(-2)+b
1=4+b
minus 3 both sides
-3=b
so the equation is
y=-2x-3
your teacher might want it in standard form (ax+by=c) so
add 2x both sides
2x+y=-3 is an equation
so y=-2x-3 is correct (slope intercept form)
2x+y=-3 is also correct (standard form)
Work is attached to this post
Answer:
1. 240 oz
2. 6000lb
3. 20 lb
4. 368 oz
5. 12000 lb
6. 9 lb
7. 30000 lb
8. 22
9. 288
Step-by-step explanation:
