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A circle has center O(2, 3) and radius 10. Which of the following points is on the circle?

Hint: \(d= \sqrt{(x1-x2)^2+(y1-y2)^2}\)

 V(−3, 2) 

X(5, −2) 

Y(2, 0) 

Z(8, 11)

sandman12345  Apr 29, 2018
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A circle has center O(2, 3) and radius 10. Which of the following points is on the circle?

Hint: \(d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

 V(−3, 2) 

X(5, −2) 

Y(2, 0) 

Z(8, 11)

 

\(\text{Let $x_c = 2$ } \\ \text{Let $y_c = 3$ } \\ \text{Let $r = 10$ }\)

 

\(\begin{array}{|lrcll|} \hline & r^2 &=& (x_p - x_c)^2 + (y_p - y_c)^2 \\\\ V(x_p=-3,y_p=2) & 100 &=& (-3 - 2)^2 + (2 - 3)^2 \\ & 100 & \ne & 25 + 1\quad \text{no} \\\\ X(x_p=5,y_p=-2) & 100 &=& (5 - 2)^2 + (-2 - 3)^2 \\ & 100 & \ne & 9 + 25 \quad \text{no} \\\\ Y(x_p=2,y_p=0) & 100 &=& (2 - 2)^2 + (0 - 3)^2 \\ & 100 & \ne & 0 + 9 \quad \text{no} \\\\ Z(x_p=8,y_p=11) & 100 &=& (8 - 2)^2 + (11 - 3)^2 \\ & 100 & = & 36 + 64 \quad \text{yes} \\ \hline \end{array}\)

 

laugh

heureka  Apr 30, 2018

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