A triangle has corners at $(6, 3)$ $(6, 3 )$ , ( 8, -2) $, and$ $, and$ (1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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A triangle has corners at $(6, 3)$ $(6, 3 )$ , ( 8, -2) $, and$ $, and$ (1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-05T10:37:09

(5 ,0)

Explanation:

The first step here is to find the coordinates of the centroid of the triangle.

Given the 3 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 centroid is calculated as follows:

$color(red)(|bar(ul(color(white)(a/a)color(black)(x_c=1/3(x_1+x_2+x_3), y_c=1/3(y_1+y_2+y_3))color(white)(a/a)|)))$

let $(x_1,y_1)=(6,3),(x_2,y_2)=(8,-2),(x_3,y_3)=(1,-1)$

$rArrx_c=1/3(6+8+1)" and " y_c=1/3(3-2-1)$

coordinates of centroid = (5 ,0)

Under a reflection in the x-axis

A point (x ,y) → (x ,-y)

Since the point (5 ,0) is on the x-axis, it's position will remain the same under a reflection in the x-axis.

hence (5 ,0) → (5 ,0)

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A triangle has corners at $(6, 3)$ $(6, 3 )$ , ( 8, -2) $, and$ $, and$ (1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

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Science

Math

Humanities

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A triangle has corners at (6, 3 )(6,3)(6, 3 ), ( 8, -2), and ,and, and (1, -1 )#. 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 $(6, 3)$ $(6, 3 )$ , ( 8, -2) $, and$ $, and$ (1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?