Question

Using two endpoints on a circle: P(5, 4) and Q (-1, 14), determine each of the following:Slope between the two points:Center of the circle:Distance between points P and Q:State what the Distance represents:State the radius of the circle:State the diameter of the circle:Find the area of the circle:

Answer 1

`\begin{gathered} 1)\text{ The slope} \\ P(5,4)\colon x_1=5,_{}y_1\text{= 4} \\ Q(-1,14)\text{ : }x_2=-1,\text{ }y_2\text{= 14 } \\ \text{Slope = }\frac{y_2\text{ - }y_1}{\text{ }x_2\text{ - }x_1\text{ }} \\ \text{Slope = }\frac{14\text{ -4}}{-1-5}\text{ = }(10)/(-6)\text{ = -}(5)/(2)\text{ = -2}(1)/(2) \end{gathered}`
`\begin{gathered} 2)\text{ Distance betwe}en\text{ PQ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{ PQ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{ PQ = }\sqrt[]{(14-4)^2+(-1_{}-5_{})^2} \\ \text{ PQ = }\sqrt[]{(14-4)^2+(-1_{}-5_{})^2} \\ \text{ PQ = }\sqrt[]{(10)^2+(-6_{})^2} \\ \text{ PQ = }\sqrt[]{100\text{ + 36}} \\ \text{ PQ = }\sqrt[]{136} \\ \text{ PQ(D) = 11.66} \\ 3)The\text{ Distance represent the DIAMETER of the circle} \\ 4)\text{ Radius = }(D)/(2)\text{ =}(11.66)/(2)\text{ = 5.83cm} \\ 5)\text{ Area =}\pi\text{ }* r^2 \\ \text{Area = }(22)/(7)\text{ }*5.83^2 \\ \text{Area = }(747.75)/(7)=106.8cm^2 \end{gathered}`
`\begin{gathered} 4)(x,y)\text{ =( }(x1+x2)/(2),\text{ }(y1+y2)/(2)) \\ \text{ = }(5-1)/(2),(14+4)/(2) \\ \text{ =(2, 9)} \end{gathered}`