Solve the Problem $\mathrm { P } _ { 1 } , \mathrm { P } _ { 2 }$

question 56

Multiple Choice

Solve the problem.
-Find the length of each side of the triangle determined by the three points $\mathrm { P } _ { 1 } , \mathrm { P } _ { 2 }$ , and $\mathrm { P } _ { 3 }$ . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both.
$$\mathrm { P } _ { 1 } = ( - 5 , - 4 ) , \mathrm { P } _ { 2 } = ( - 3,4 ) , \mathrm { P } _ { 3 } = ( 0 , - 1 )$$

• A) \(\mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 2 } \right) = 2 \sqrt { 17 } ; \mathrm { d } \left( \mathrm { P } _ { 2 } , \mathrm { P } _ { 3 } \right) = \sqrt { 34 } ; \mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 3 } \right) = 5 \sqrt { 2 }\)
• neither
• B) \(\mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 2 } \right) = 2 \sqrt { 17 } ; \mathrm { d } \left( \mathrm { P } _ { 2 } , \mathrm { P } _ { 3 } \right) = \sqrt { 34 } ; \mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 3 } \right) = 5 \sqrt { 2 }\)
• right triangle
• C) \(\mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 2 } \right) = 2 \sqrt { 17 } ; \mathrm { d } \left( \mathrm { P } _ { 2 } , \mathrm { P } _ { 3 } \right) = \sqrt { 34 } ; \mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 3 } \right) = \sqrt { 34 }\)
• both
• D) \(\mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 2 } \right) = 2 \sqrt { 17 } ; \mathrm { d } \left( \mathrm { P } _ { 2 } , \mathrm { P } _ { 3 } \right) = \sqrt { 34 } ; \mathrm { d } \left( \mathrm { P } _ { 1 } , \mathrm { P } _ { 3 } \right) = \sqrt { 34 }\)
• isosceles triangle

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