find the midpoint of the line segment with endpoints (\sqrt{98}, 3) and (\sqrt{2}, -3).

the midpoint of the line segment is .
(type an ordered pair. type an exact answer for each coordinate, using radicals as needed.)

Question

find the midpoint of the line segment with endpoints (\sqrt{98}, 3) and (\sqrt{2}, -3).

the midpoint of the line segment is  .
(type an ordered pair. type an exact answer for each coordinate, using radicals as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Midpoint Formula", "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Midpoint Formula", "Radical Simplification" ] } ## Simplify the radical coordinates Using the *Radical Simplification* knowledge point $$ \sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2} $$ ## Apply the midpoint formula Using the *Midpoint Formula* knowledge point $$ \begin{aligned} x_m &= \frac{7\sqrt{2} + \sqrt{2}}{2} = \frac{8\sqrt{2}}{2} = 4\sqrt{2}\ y_m &= \frac{3 + (-3)}{2} = \frac{0}{2} = 0 \end{aligned} $$ ## State the final coordinates Using the *Midpoint Formula* knowledge point $$ (x_m, y_m) = (4\sqrt{2}, 0) $$ The midpoint of the line segment is $(4\sqrt{2}, 0)$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Midpoint Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the radical coordinates

Apply the midpoint formula

State the final coordinates

Answer: