question 3 of 25

what is the distance between the points $(22, 27)$ and $(2, -10)$? if necessary, round your answer to two decimal places.

a. 42.06 units
b. 37 units
c. 31.13 units
d. 57 units

Question

question 3 of 25

what is the distance between the points $(22, 27)$ and $(2, -10)$? if necessary, round your answer to two decimal places.

a. 42.06 units
b. 37 units
c. 31.13 units
d. 57 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Coordinate Geometry" ] } ## Identify coordinates and formula $$ \begin{aligned} &(x_1, y_1) = (22, 27)\ &(x_2, y_2) = (2, -10)\ &d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \end{aligned} $$ ## Substitute and simplify $$ \begin{aligned} &d = \sqrt{(2 - 22)^2 + (-10 - 27)^2}\ &d = \sqrt{(-20)^2 + (-37)^2}\ &d = \sqrt{400 + 1369}\ &d = \sqrt{1769} \end{aligned} $$ ## Calculate final decimal value $$ \begin{aligned} &d \approx 42.05948...\ &d \approx 42.06\text{ units} \end{aligned} $$

A. 42.06 units

B. 37 units

C. 31.13 units

D. 57 units

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

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QUESTION IMAGE

Question

Explanation:

Identify coordinates and formula

Substitute and simplify

Calculate final decimal value

Answer: