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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Selling Price

The price at which a product or service is sold to customers, determined by factors like cost, demand, competition, and market conditions.

Variable Costs

Expenses that vary in relation to the amount of products or services a company generates.

Short Run

A period in which at least one input is fixed and cannot be changed by the firm.

Variable Costing

A cost accounting method that includes only variable costs—costs that change with production levels—in product cost calculations.