the coordinates of midpoint m and endpoint c of a segment are m(25.4, 60.1) and c(18.3, 72.5). find the coordinates of the other endpoint.

(11.2, 84.9)
(21.85, 66.3)
(32.5, 47.7)
(37.8, 53)

Question

the coordinates of midpoint m and endpoint c of a segment are m(25.4, 60.1) and c(18.3, 72.5). find the coordinates of the other endpoint.

(11.2, 84.9)
(21.85, 66.3)
(32.5, 47.7)
(37.8, 53)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Midpoint Formula", "Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Midpoint Formula", "Coordinate Geometry" ] } ## Set up midpoint equations for the unknown endpoint $D(x, y)$ $$ \begin{aligned} M(x_m, y_m) &= (25.4, 60.1) \ C(x_c, y_c) &= (18.3, 72.5) \ \frac{x + 18.3}{2} &= 25.4 \ \frac{y + 72.5}{2} &= 60.1 \end{aligned} $$ ## Solve for the x-coordinate $$ \begin{aligned} x + 18.3 &= 50.8 \ x &= 50.8 - 18.3 \ x &= 32.5 \end{aligned} $$ ## Solve for the y-coordinate $$ \begin{aligned} y + 72.5 &= 120.2 \ y &= 120.2 - 72.5 \ y &= 47.7 \end{aligned} $$

(A) $(11.2, 84.9)$

(B) $(21.85, 66.3)$

(C) $(32.5, 47.7)$

(D) $(37.8, 53)$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up midpoint equations for the unknown endpoint \(D(x, y)\)

Solve for the x-coordinate

Solve for the y-coordinate

Answer: