current objective
use the distance formula to find the distance between two points

question
use the distance formula to find the distance between the points $(10, -9)$ and $(1, -1)$.

(write your answer in exact form.)

provide your answer below:

Question

current objective
use the distance formula to find the distance between two points

question
use the distance formula to find the distance between the points $(10, -9)$ and $(1, -1)$.

(write your answer in exact form.)

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula" ], "new_concepts": [], "current_concepts": [ "Distance Formula" ] } ## Apply the distance formula $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ ## Substitute the given coordinates $$ \begin{aligned} (x_1, y_1) &= (10, -9) \ (x_2, y_2) &= (1, -1) \ d &= \sqrt{(1 - 10)^2 + (-1 - (-9))^2} \end{aligned} $$ ## Simplify the expression $$ \begin{aligned} d &= \sqrt{(-9)^2 + (8)^2} \ d &= \sqrt{81 + 64} \ d &= \sqrt{145} \end{aligned} $$ Use the distance formula to find the distance between the points $(10, -9)$ and $(1, -1)$. (Write your answer in exact form.) Provide your answer below: $\sqrt{145}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the distance formula

Substitute the given coordinates

Simplify the expression

Answer: