2. use the distance formula to find the lengths of the sides of the second triangle, $\delta stu$.

$su = \sqrt{(-2 - (-8))^2 + (-7 - (-3))^2} = \sqrt{6^2 + (-4)^2} = \sqrt{36 + 16} = \sqrt{52} = \sqrt{4(13)} = 2\sqrt{13}$

the length of $\overline{st}$ is 5. what is the length of $\overline{tu}$?

$\bigcirc \sqrt{53}$
$\bigcirc \sqrt{85}$
$\bigcirc \sqrt{45}$

Question

2. use the distance formula to find the lengths of the sides of the second triangle, $\delta stu$.

$su = \sqrt{(-2 - (-8))^2 + (-7 - (-3))^2} = \sqrt{6^2 + (-4)^2} = \sqrt{36 + 16} = \sqrt{52} = \sqrt{4(13)} = 2\sqrt{13}$

the length of $\overline{st}$ is 5. what is the length of $\overline{tu}$?

$\bigcirc \sqrt{53}$
$\bigcirc \sqrt{85}$
$\bigcirc \sqrt{45}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Coordinate Geometry" ] } ## Identify coordinates of points T and U $$ \begin{aligned} T &= (-4, 0) \ U &= (-2, -7) \end{aligned} $$ ## Apply the distance formula to find TU $$ \begin{aligned} TU &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ TU &= \sqrt{(-2 - (-4))^2 + (-7 - 0)^2} \ TU &= \sqrt{(2)^2 + (-7)^2} \ TU &= \sqrt{4 + 49} \ TU &= \sqrt{53} \end{aligned} $$

(A) $\sqrt{53}$

(B) $\sqrt{85}$

(C) $\sqrt{45}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of points T and U

Apply the distance formula to find TU

Answer: