what is the distance between the points $(7, 8)$ and $(-8, 0)$ on a coordinate grid?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Pythagorean Theorem" ] } ## Identify coordinates and formula $$ \begin{aligned} &(x_1, y_1) = (7, 8)\ &(x_2, y_2) = (-8, 0)\ &d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \end{aligned} $$ ## Substitute values and simplify $$ \begin{aligned} &d = \sqrt{(-8 - 7)^2 + (0 - 8)^2}\ &d = \sqrt{(-15)^2 + (-8)^2}\ &d = \sqrt{225 + 64} \end{aligned} $$ ## Calculate final distance $$ \begin{aligned} &d = \sqrt{289}\ &d = 17 \end{aligned} $$ What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid? 17 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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Explanation:

Identify coordinates and formula

Substitute values and simplify

Calculate final distance

Answer: