Answer to Question #126525 in Algebra for Tasmyn

Question

Answer the following prompts with numerical answers only. If necessary, round answers to the nearest tenth of a unit.
The diameter of circle P has endpoints A(-1, 5) and B(4, -3).

Use the midpoint formula to find the coordinates of the center of the circle, P(x,y).
P(a0, a1)
Use the distance formula to find the length of the radius of circle P. The length of the radius of circle P is a2 units.
Using 3.14 to approximate , the circumference of circle P. The circumference of circle P is approximately a3 units.
Using 3.14 to approximate , the area of circle P is approximately a4 square units.

Answer 1

Let the circle be shown as attached in the screenshot.

so as per question: A= $\lparen-1,5\rparen$ and B = $\lparen4,-3\rparen$

mid point formula = $\lparen [x_{1} +x_{2}] \div2 , [y_{1} +y_{2}] \div2\rparen$

$\therefore$ coordinates of centre of circle = $\lparen [-1 +4] \div2 , [5-3] \div2\rparen$

= $\lparen1.5,1\rparen$

distance formula between two points $\lparen x_{1},x_{2}\rparen$ and $\lparen y_{1},y_{2}\rparen$ = $\sqrt{\lparen{y_{2}-y_{1}\rparen}^{2} + \lparen{x_{2}-x_{1}\rparen}^{2}}$

$\therefore$ radius of circle = $Diameter \div 2$

so radius of the circle = $\sqrt{\lparen{4-{-1}\rparen}^{2} + \lparen{-3-5\rparen}^{2}} \div 2$

= $\sqrt{25 +64} \div 2$

= $\sqrt89 \div 2$

=$9.43\div 2$

= $4.71$

$\approx 5$

Circumference of a circle = $2\pi r$ where r is the radius of circle

= $2* 3.14 * 5$

= $\approx 31$

Area of circle = $\pi r^{2}$ where r is the radius of circle

= $3.14 *\lparen5\rparen^{2}$

= $3.14 * 25$

= $78.5$

$\approx 79$