find the other endpoint of the line segment with the given endpoint and midpoint.
endpoint: $(3, -9)$, midpoint: $(-10, 9)$
endpoint = ( , )

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Midpoint Formula", "Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Midpoint Formula", "Coordinate Geometry" ] } ## Set up the midpoint equations $$ \begin{aligned} (x_1, y_1) &= (3, -9) \ (x_m, y_m) &= (-10, 9) \ x_m &= \frac{x_1 + x_2}{2} \ y_m &= \frac{y_1 + y_2}{2} \end{aligned} $$ ## Solve for the x-coordinate of the other endpoint $$ \begin{aligned} -10 &= \frac{3 + x_2}{2} \ -20 &= 3 + x_2 \ x_2 &= -23 \end{aligned} $$ ## Solve for the y-coordinate of the other endpoint $$ \begin{aligned} 9 &= \frac{-9 + y_2}{2} \ 18 &= -9 + y_2 \ y_2 &= 27 \end{aligned} $$ Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (3, -9), midpoint: (-10, 9) Endpoint = ( -23 , 27 ) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Midpoint Formula" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the midpoint equations

Solve for the x-coordinate of the other endpoint

Solve for the y-coordinate of the other endpoint

Answer: