[tex] \huge{ \color{green}{ \mathcal{Answers:}}}[/tex]
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I. Give the following distance.
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1. X(-3,9) and Y(2,5)
Formula:
[tex] \tt \large \: d = \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]
Given:
[tex] \tt \large x_{1} = - 3[/tex]
[tex] \large \tt x_{2} = 2[/tex]
[tex] \large \tt \: y_{1} = 9[/tex]
[tex] \large \tt \: y_{2} = 5[/tex]
Solution:
[tex] \tt \: d = \sqrt{(x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]
[tex] \tt \: d = \sqrt{(2 - ( - 3))^{2} + (5 - 9) ^{2} } [/tex]
[tex] \tt \: d = \sqrt{( {5})^{2} + ( - 4) ^{2} } [/tex]
[tex] \tt \: d = \sqrt{25 + 16} [/tex]
[tex] \large \green{ \boxed{ \boxed{ \tt {\: d = \sqrt{41} }}}}[/tex]
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2. C(-3, 2) and D(9,7)
Formula:
• Same as Number 1.
Given:
[tex] \large \tt x_{1} = - 3[/tex]
[tex] \large \tt x_{2} = 9[/tex]
[tex] \large \tt y_{1} = 2[/tex]
[tex] \large \tt y_{2} = 7[/tex]
Solution:
[tex] \tt \: d = \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1}) ^{2} } [/tex]
[tex] \tt \: d = \sqrt{(9 - ( - 3))^{2} + (7 - 2)^{2} } [/tex]
[tex] \tt \: d = \sqrt{(12)^{2} + (5)^{2} } [/tex]
[tex] \tt \: d = \sqrt{144 + 25} [/tex]
[tex] \tt \: d = \sqrt{169} [/tex]
[tex] \large \green{ \boxed{ \boxed{ \tt{d = 13}}}}[/tex]
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III - Give the following midpoint.
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1. A(6, 8) and B( 12, 10)
Formula:
[tex] \large \tt \: M = ( \frac{ x_{1} + x_{2}}{2} \: , \frac{ y_{1} + y_{2} }{2} )[/tex]
Given:
[tex] \large \tt \: x_{1} = 6[/tex]
[tex] \large \tt \: x_{2} = 12[/tex]
[tex] \large \tt \: y_{1} = 8[/tex]
[tex] \large \tt \: y_{2} = 10 [/tex]
Solution:
[tex] \large \tt \: M = ( \frac{ x_{1} + x_{2}}{2} \: , \frac{ y_{1} + y_{2} }{2} )[/tex]
[tex] \large \tt \: M = ( \frac{6 + 12}{2} \: , \: \frac{8 + 10}{2} )[/tex]
[tex] \large \tt \: M = ( \frac{18}{2} \: , \: \frac{18}{2} )[/tex]
[tex] \large \red{ \boxed{ \boxed{ \tt{M = (9,9)}}}}[/tex]
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2. C(5, 11) and D(9,5)
Formula:
• Same as Number 1.
Given:
[tex] \large \tt \: x_{1} = 5[/tex]
[tex] \large \tt \: x_{2} = 9[/tex]
[tex] \large \tt \:y_{1} = 11 [/tex]
[tex] \large \tt \: y_{2} = 5[/tex]
Solution:
[tex] \large \tt \: M = ( \frac{ x_{1} + x_{2}}{2} \: , \frac{ y_{1} + y_{2} }{2} )[/tex]
[tex] \large \tt \: M = ( \frac{5 + 9}{2} \: , \: \frac{11 + 5}{2} )[/tex]
[tex] \large \tt \: M = ( \frac{14}{2} \: , \: \frac{16}{2} )[/tex]
[tex] \large \red{ \boxed{ \boxed{ \tt{ M = (7,8)}}}}[/tex]
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