A triangle has corners at $(3, 5)$ $(3, 5 )$ , ( 6, 2) $, and$ $, and$ ( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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A triangle has corners at $(3, 5)$ $(3, 5 )$ , ( 6, 2) $, and$ $, and$ ( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2018-04-22T14:31:43

$(\frac{13}{3}, - \frac{10}{3})$ $(13/3,-10/3)$

Explanation:

$given the coordinates of the vertices of a triangle$ $"given the coordinates of the vertices of a triangle"$

$(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ $(x_1,y_1),(x_2,y_2),(x_3,y_3)$

$then the coordinates of the centroid are$ $"then the coordinates of the centroid are"$

$∙ x [\frac{1}{3} (x_{1} + x_{2} + x_{3}), \frac{1}{3} (y_{1} + y_{2} + y_{3})]$ $•color(white)(x)[1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3)]$

$here (x_{1}, y_{1}) = (3, 5), (x_{2}, y_{2}) = (6, 2), (x_{3}, y_{3}) = (4, 3)$ $"here "(x_1,y_1)=(3,5),(x_2,y_2)=(6,2),(x_3,y_3)=(4,3)$

$hence coordinates of centroid are$ $"hence coordinates of centroid are"$

$[\frac{1}{3} (3 + 6 + 4), \frac{1}{3} (5 + 2 + 3)] = (\frac{13}{3}, \frac{10}{3})$ $[1/3(3+6+4),1/3(5+2+3)]=(13/3,10/3)$

$under a reflection in the x-axis$ $"under a reflection in the x-axis"$

$∙ a point (x, y) \to (x, - y)$ $• " a point "(x,y)to(x,-y)$

$\Rightarrow (\frac{13}{3}, \frac{10}{3}) \to (\frac{13}{3}, - \frac{10}{3}) \leftarrow new centroid$ $rArr(13/3,10/3)to(13/3,-10/3)larrcolor(red)"new centroid"$

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A triangle has corners at $(3, 5)$ $(3, 5 )$ , ( 6, 2) $, and$ $, and$ ( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

A triangle has corners at (3,5)(3, 5 ), ( 6, 2),and, and ( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

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Impact of this question

A triangle has corners at $(3, 5)$ $(3, 5 )$ , ( 6, 2) $, and$ $, and$ ( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?