Answer:
The area of this " imaginary " circle is [tex]193\pi[/tex]
Step-by-step explanation:
Point P, or ( - 3, 4 ) acts as our center point, whereas point Q, ( 9, - 3 ) is a point on the circumference of this " circle. " Therefore, the distance between the two points should be the radius of circle. Let's apply the distance formula to determine the distance between the two points / the radius of this imaginary circle. Afterwards we can determine the circle's area through the formula [tex]\pi r^2[/tex].
Distance between point ( - 3, 4 ) and ( 9, - 3 )
= [tex]\sqrt{(9 - ( - 3 ) )^2 + (-3-4)^2}[/tex]
= [tex]\sqrt{(12)^2+(-7)^2}[/tex]
= [tex]\sqrt{144+49}[/tex] = [tex]\sqrt{193}[/tex]
Therefore, the radius = [tex]\sqrt{193}[/tex] . This would make the area of the circle the following ...
Area of circle
= [tex]\pi r^2[/tex] = [tex]\pi ( \sqrt{193} )^2[/tex] = [tex]193\pi[/tex] - ... which is our solution.
