when graphed on a coordinate plane beths house is located at $(4, 3)$ and the coffee shop is located at the point $(-2, -1)$. what is the distance from beths house to the coffee shop? each grid line on the coordinate plane represents 1 mile.

$\bigcirc$ 10 miles
$\bigcirc$ $\sqrt{8}$ miles
$\bigcirc$ $\sqrt{52}$ miles
$\bigcirc$ 52 miles

Question

when graphed on a coordinate plane beths house is located at \$(4, 3)\$ and the coffee shop is located at the point \$(-2, -1)\$. what is the distance from beths house to the coffee shop? each grid line on the coordinate plane represents 1 mile.

\$\bigcirc\$ 10 miles
\$\bigcirc\$ \$\sqrt{8}\$ miles
\$\bigcirc\$ \$\sqrt{52}\$ miles
\$\bigcirc\$ 52 miles

$\bigcirc$ 10 miles
$\bigcirc$ $\sqrt{8}$ miles
$\bigcirc$ $\sqrt{52}$ miles
$\bigcirc$ 52 miles

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Distance Formula" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Pythagorean Theorem" ] } ## Identify the coordinates of the two points $$ (x_1, y_1) = (4, 3),\quad (x_2, y_2) = (-2, -1) $$ ## Apply the distance formula $$ \begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ d &= \sqrt{(-2 - 4)^2 + (-1 - 3)^2} \ d &= \sqrt{(-6)^2 + (-4)^2} \ d &= \sqrt{36 + 16} \ d &= \sqrt{52} \end{aligned} $$

(A) 10 miles

(B) $\sqrt{8}$ miles

(C) $\sqrt{52}$ miles

(D) 52 miles

{ "elements": [ { "type": "point", "params": [[4, 3]], "properties": { "name": "Beth's House (4, 3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-2, -1]], "properties": { "name": "Coffee Shop (-2, -1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "segment", "params": [[4, 3], [-2, -1]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3, "name": "d = \sqrt{52}", "withLabel": true } }, { "type": "segment", "params": [[-2, -1], [4, -1]], "properties": { "strokeColor": "#F28A55", "strokeWidth": 2, "strokeDash": 2 } }, { "type": "segment", "params": [[4, -1], [4, 3]], "properties": { "strokeColor": "#F28A55", "strokeWidth": 2, "strokeDash": 2 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the two points

Apply the distance formula

Answer: