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3 years ago

The coordinates of the endpoints of line segment C D are C(3, 8) and D(6, -1). Express the length of line segment C D in simples

t radical form.

Mathematics

1 answer:

8_murik_8 [283]3 years ago

3 0

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
C&({{ 3}}\quad ,&{{ 8}})\quad 
% (c,d)
D&({{ 6}}\quad ,&{{ -1}})
\end{array}\qquad 
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
CD=\sqrt{(6-3)^2+(-1-8)^2}\implies CD=\sqrt{3^2+(-9)^2}
\\\\\\
CD=\sqrt{9+81}\implies CD=\sqrt{90}\quad 
\begin{cases}
90=2\cdot 3\cdot 3\cdot 5\\
\qquad 2\cdot 3^2\cdot 5\\
\qquad 10\cdot 3^2
\end{cases}
\\\\\\
CD=\sqrt{10\cdot 3^2}\implies CD=3\sqrt{10}$

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Given that the options of the set of ordered pairs.

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From this set of ordered pairs, it is obvious that the element -12 of x is related to two different element in y.

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Hence, Option A is not the correct answer.

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From this set of ordered pairs, it is obvious that the elements -8 and 8 of x are related to two different element in y.

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Hence, Option B is not the correct answer.

Option C: $\{(13,-3),(13,0),(13,-1),(13,-1)\}$

From this set of ordered pairs, it is obvious that the element 13 of x is related to three different element in y.

Thus, the ordered pairs $\{(13,-3),(13,0),(13,-1),(13,-1)\}$ is not a function.

Hence, Option C is not the correct answer.

Option D: $\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}$

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From this set of ordered pairs, it is obvious that the each element of x is related exactly one element in y.

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