Solve the Problem $$\mathrm { P } _ { 1 } , \mathrm { P } _ { 2 } \text {, and } \mathrm { P } _ { 3 }$$

question 18

Multiple Choice

Solve the problem.
-Find the length of each side of the triangle determined by the three points $$\mathrm { P } _ { 1 } , \mathrm { P } _ { 2 } \text {, and } \mathrm { P } _ { 3 }$$ . 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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Definitions:

Unfreezing

The initial phase in the process of change, where existing beliefs and behaviors are questioned, making room for new ways of thinking.

Lewin's Basic Change Model

A theoretical framework by Kurt Lewin that describes organizational change as a process of unfreezing, changing, and refreezing behavior and practices.

DADA Syndrome

Four stages—denial, anger, depression, and acceptance—experienced by individuals when they are faced with unwanted change.

Denial

A psychological defense mechanism wherein an individual refuses to accept reality or facts.