what is the distance between $(-6, 2)$ and $(8, 10)$ on a coordinate grid?

* $\sqrt{60}$
* $\sqrt{68}$
* $\sqrt{162}$
* $\sqrt{260}$

Question

what is the distance between $(-6, 2)$ and $(8, 10)$ on a coordinate grid?

* $\sqrt{60}$
* $\sqrt{68}$
* $\sqrt{162}$
* $\sqrt{260}$

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" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Coordinate Geometry" ] } ## Identify coordinates and distance formula $$ \begin{aligned} &(x_1, y_1) = (-6, 2)\ &(x_2, y_2) = (8, 10)\ &d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \end{aligned} $$ ## Substitute values into the formula $$ \begin{aligned} &d = \sqrt{(8 - (-6))^2 + (10 - 2)^2}\ &d = \sqrt{(8 + 6)^2 + (8)^2} \end{aligned} $$ ## Simplify the expression $$ \begin{aligned} &d = \sqrt{14^2 + 8^2}\ &d = \sqrt{196 + 64}\ &d = \sqrt{260} \end{aligned} $$

(A) $\sqrt{60}$

(B) $\sqrt{68}$

(C) $\sqrt{162}$

(D) $\sqrt{260}$

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

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QUESTION IMAGE

Question

Explanation:

Identify coordinates and distance formula

Substitute values into the formula

Simplify the expression

Answer: