Question

puntos posibles: 6.67
a hiking trail map is placed on a coordinate grid. the ranger station is at the origin. the waterfall is 3 miles west and 7 miles north of the ranger station.
the campsite is 5 miles east and 2 miles north of the ranger station.

○ $\triangle wcr$ is a scalene triangle
○ $\triangle wcr$ is a right scalene triangle
○ $\triangle wcr$ is a right isosceles triangle
○ there is not enough information to determine what type of triangle $\triangle wcr$ is.

Explanation:

Step1: Asignar coordenadas a cada punto

Estación guardabosques (R): $(0,0)$; Cascada (W): $(3,7)$; Campamento (C): $(5,2)$

Step2: Calcular longitud WR

Usar fórmula de distancia: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$\overline{WR}=\sqrt{(3-0)^2+(7-0)^2}=\sqrt{9+49}=\sqrt{58}$

Step3: Calcular longitud RC

$\overline{RC}=\sqrt{(5-0)^2+(2-0)^2}=\sqrt{25+4}=\sqrt{29}$

Step4: Calcular longitud WC

$\overline{WC}=\sqrt{(5-3)^2+(2-7)^2}=\sqrt{4+25}=\sqrt{29}$

Step5: Verificar ángulo recto

Usar teorema de Pitágoras: $(\sqrt{29})^2+(\sqrt{29})^2=29+29=58=(\sqrt{58})^2$

Step6: Clasificar triángulo

Dos lados iguales, ángulo recto.

Answer:

$\boldsymbol{\triangle WCR}$ is a right isosceles triangle