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# proofs on the coordinate plane

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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)

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

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

heureka  Apr 30, 2018