use the pythagorean theorem to find the distance between $(1, 3)$ and $(-4, -2)$. write the answer as a decimal and round to the nearest hundredth.

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem Coordinate Geometry", "Distance Formula" ] } ## Find the horizontal and vertical distances $$ \begin{aligned} a &= |1 - (-4)| = 5 \ b &= |3 - (-2)| = 5 \end{aligned} $$ ## Apply the Pythagorean Theorem $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 5^2 + 5^2 \ c^2 &= 25 + 25 = 50 \ c &= \sqrt{50} \end{aligned} $$ ## Calculate and round the decimal value $$ \begin{aligned} c &\approx 7.0710678... \ c &\approx 7.07 \end{aligned} $$ Use the Pythagorean Theorem to find the distance between (1, 3) and (-4, -2). Write the answer as a decimal and round to the nearest hundredth. 7.07 { "elements": [ { "type": "point", "params": [[1, 3]], "properties": { "name": "(1, 3)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[-4, -2]], "properties": { "name": "(-4, -2)", "size": 4, "color": "#5583F2", "withLabel": true } }, { "type": "segment", "params": [[1, 3], [-4, -2]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "dash": 0 } }, { "type": "segment", "params": [[-4, -2], [1, -2]], "properties": { "strokeColor": "#55DDF2", "strokeWidth": 2, "dash": 2 } }, { "type": "segment", "params": [[1, -2], [1, 3]], "properties": { "strokeColor": "#55DDF2", "strokeWidth": 2, "dash": 2 } }, { "type": "point", "params": [[1, -2]], "properties": { "name": "", "size": 2, "color": "#55DDF2", "withLabel": false } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem Coordinate Geometry" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the horizontal and vertical distances

Apply the Pythagorean Theorem

Calculate and round the decimal value

Answer: