Question

draw a circle with center (-1, 3 ) and radius of 2.

Explanation:

Step1: Locate the center

The center of the circle is at the point \((-1,3)\). On the coordinate grid, move 1 unit to the left of the y - axis (since \(x=-1\)) and 3 units up from the x - axis (since \(y = 3\)) to mark the center.

Step2: Determine points on the circle

The radius \(r = 2\). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for a circle \((x - h)^2+(y - k)^2=r^2\) (where \((h,k)=(-1,3)\) and \(r = 2\)).

• Points horizontally and vertically from the center:
• Moving 2 units to the right from the center \((-1,3)\): the point is \((-1 + 2,3)=(1,3)\)
• Moving 2 units to the left from the center \((-1,3)\): the point is \((-1-2,3)=(-3,3)\)
• Moving 2 units up from the center \((-1,3)\): the point is \((-1,3 + 2)=(-1,5)\)
• Moving 2 units down from the center \((-1,3)\): the point is \((-1,3-2)=(-1,1)\)
• Points using the Pythagorean relationship (for a more accurate circle drawing):

Let \(x=-1 + a\) and \(y=3 + b\) such that \(a^{2}+b^{2}=4\). For example, if \(a=\sqrt{3}\approx1.73\) and \(b = 1\), then one point is \((-1+\sqrt{3},3 + 1)\approx(0.73,4)\) and another is \((-1-\sqrt{3},3 + 1)\approx(-2.73,4)\), \((-1+\sqrt{3},3 - 1)\approx(0.73,2)\) and \((-1-\sqrt{3},3 - 1)\approx(-2.73,2)\)

Step3: Draw the circle

Connect all the points (the center - related points and the additional points) smoothly to form a circle.

Answer:

Follow the above steps to draw a circle with center \((-1,3)\) and radius \(2\) on the given coordinate grid.