use the pythagorean theorem to find the distance between (-5, 3) and (-3, -2).

* $\sqrt{29}$
* none of the above
* 29
* 5

Question

use the pythagorean theorem to find the distance between (-5, 3) and (-3, -2).

* $\sqrt{29}$
* none of the above
* 29
* 5

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem Coordinate Geometry", "Distance Formula" ] } ## Calculate horizontal and vertical distances $$ \begin{aligned} a &= |x_2 - x_1| = |-3 - (-5)| = 2 \ b &= |y_2 - y_1| = |-2 - 3| = 5 \end{aligned} $$ ## Apply the Pythagorean Theorem $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 2^2 + 5^2 \ c^2 &= 4 + 25 = 29 \ c &= \sqrt{29} \end{aligned} $$

(A) $\sqrt{29}$

(B) None of the above

(C) 29

(D) 5

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QUESTION IMAGE

Question

Explanation:

Calculate horizontal and vertical distances

Apply the Pythagorean Theorem

Answer: