Answer:
The coordinates of the circumcenter of this triangle are (3,2)
Step-by-step explanation:
we know that
The circumcenter is the point where the perpendicular bisectors of a triangle intersect
we have the coordinates

step 1
Find the midpoint AB
The formula to calculate the midpoint between two points is equal to

substitute the values


step 2
Find the equation of the line perpendicular to the segment AB that passes through the point (-2,2)
Is a horizontal line (parallel to the x-axis)
-----> equation A
step 3
Find the midpoint BC
The formula to calculate the midpoint between two points is equal to

substitute the values


step 4
Find the equation of the line perpendicular to the segment BC that passes through the point (3,-1)
Is a vertical line (parallel to the y-axis)
-----> equation B
step 5
Find the circumcenter
The circumcenter is the intersection point between the equation A and equation B
-----> equation A
-----> equation B
The intersection point is (3,2)
therefore
The coordinates of the circumcenter of this triangle are (3,2)
Slope = rise/run = (change in y)/(change in x)
Slope = (4-6)/(0-(-4)) = (-2)/(4)
Slope = -1/2 = -0.5
Answer:
<h2>f(x) = 3x + 4</h2>
Step-by-step explanation:
f(x + 1) = 3x - 7
f(x) = f(x + 1 - 1) = 3(x - 1) + 7 = 3x - 3 + 7 = 3x + 4
Check
f(x) = 3x + 4
f(x + 1) = 3(x + 1) + 4 = 3x + 3 + 4 = 3x + 7 CORRECT
Answer:
The y intercept is -1
Step-by-step explanation:
the y-intercept is when y = 0
f(0) = -2^2 + 4(0) - 5
f(0) = 4 - 5
f(0) = -1