Question

11.1: distance and midpoint formulas; circles
score: 11/24 answered: 9/18
question 10
draw a circle with an equation of ((x - 3)^2 + (y + 1)^2 = 4^2).

Explanation:

Step1: Identify the center of the circle

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center. For the equation \((x - 3)^2+(y+1)^2 = 4^2\), we have \(h = 3\) and \(k=-1\). So the center is \((3,-1)\).

Step2: Identify the radius of the circle

From the equation \((x - 3)^2+(y + 1)^2=4^2\), comparing with \((x - h)^2+(y - k)^2=r^2\), we get \(r = 4\).

Step3: Plot the center and draw the circle

• Plot the point \((3,-1)\) on the coordinate plane.
• From the center \((3,-1)\), move 4 units up (to \((3,3)\)), 4 units down (to \((3,-5)\)), 4 units left (to \((-1,-1)\)) and 4 units right (to \((7,-1)\)).
• Sketch the circle passing through these four points.

Answer:

Plot the center at \((3,-1)\) and draw a circle with radius \(4\) units.