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$\delta abc$ has vertices at $a(-3, 7)$, $b(4, 8)$, and $c(1, -2)$. the triangle is dilated by a factor of 3 with the center of dilation at vertex b, resulting in $\delta abc$. what is $bc$? round to the nearest hundredth.

$bc \approx$ choose an answer units

Question

select the correct answer from the drop-down menu.

$\delta abc$ has vertices at $a(-3, 7)$, $b(4, 8)$, and $c(1, -2)$. the triangle is dilated by a factor of 3 with the center of dilation at vertex b, resulting in $\delta abc$. what is $bc$? round to the nearest hundredth.

$bc \approx$ choose an answer units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Dilation in Coordinate Plane" ], "new_concepts": [ "Distance Formula", "Dilation Properties" ], "current_concepts": [ "Dilation in Coordinate Plane", "Distance Formula", "Dilation Properties" ] } ## Calculate the length of segment BC $$ \begin{aligned} B(4, 8), &\quad C(1, -2) \ BC &= \sqrt{(1 - 4)^2 + (-2 - 8)^2} \ BC &= \sqrt{(-3)^2 + (-10)^2} \ BC &= \sqrt{9 + 100} \ BC &= \sqrt{109} \end{aligned} $$ ## Apply the scale factor of dilation $$ \begin{aligned} \text{Scale factor } k &= 3 \ B'C' &= k \cdot BC \ B'C' &= 3\sqrt{109} \end{aligned} $$ ## Compute the numerical value rounded to the nearest hundredth $$ \begin{aligned} \sqrt{109} &\approx 10.4403 \ B'C' &\approx 3 \cdot 10.4403 \ B'C' &\approx 31.3209 \ B'C' &\approx 31.32 \end{aligned} $$ $\triangle ABC$ has vertices at $A(-3, 7)$, $B(4, 8)$, and $C(1, -2)$. The triangle is dilated by a factor of 3 with the center of dilation at vertex B, resulting in $\triangle A'B'C'$. What is $B'C'$? Round to the nearest hundredth. $B'C' \approx$ 31.32 units { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Dilation in Coordinate Plane" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the length of segment BC

Apply the scale factor of dilation

Compute the numerical value rounded to the nearest hundredth

Answer: