A triangle has corners at $(3, 8)$ $(3, 8 )$ , ( 5, -2) $, and$ $, and$ ( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Question

A triangle has corners at $(3, 8)$ $(3, 8 )$ , ( 5, -2) $, and$ $, and$ ( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Impact of this question

2020 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-14T12:50:26

Coordinates of centroid will be $(3, - \frac{5}{3})$ $(3,-5/3)$

Explanation:

The centroid of a triangle whose vertices are $(x_{1}, y_{1})$ $(x_1,y_1)$ , (x_2,y_2) $and (x_{3}, y_{3})$ $and (x_3,y_3)$ is given by

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

Hence centrid of given triangle is $(\frac{3 + 5 + 1}{3}, \frac{8 + (- 2) + (- 1)}{3})$ $((3+5+1)/3,(8+(-2)+(-1))/3)$ or $(3, \frac{5}{3})$ $(3,5/3)$ .

Now, when a point $(x, y)$ $(x,y)$ is reflected across the $x$ $x$ -axis, its coordinates become $(x, - y)$ $(x,-y)$ and hence

New coordinates are $(3, - 8)$ $(3,-8)$ , $(5, 2)$ $(5,2)$ and $(1, 1)$ $(1,1)$ and even
coordinates of centroid will have same rule.

Coordinates of centroid will be $(3, - \frac{5}{3})$ $(3,-5/3)$

Science

Math

Humanities

... and beyond

A triangle has corners at $(3, 8)$ $(3, 8 )$ , ( 5, -2) $, and$ $, and$ ( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has corners at (3,8)(3, 8 ), ( 5, -2),and, and ( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has corners at $(3, 8)$ $(3, 8 )$ , ( 5, -2) $, and$ $, and$ ( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?