The coordinate of centroid of a triangle is (1,3) and its two vertices are (-7,6) and (8,5) . find the third vertex of the triangle.
Please give me answer
It is much more important to understand how you get that answer.
Make a sketch of your triangle.
The centroid is the intersection of all 3 medians of a triangle, two would be sufficient.
A median of a triangle is a line running from a vertex to the midpoint of the opposite side.
The centroid divides the median into segments in the ratio of 2 : 1, where the longer side
is the segment from the vertex to the centroid.
To find the third vertex of the triangle, we need to use the centroid formula, which states that the coordinates of the centroid are the average of the coordinates of the three vertices of the triangle.
Let's denote the coordinates of the third vertex as (x, y).
Given:
Coordinate of the centroid = (1, 3)
Coordinates of the two vertices = (-7, 6) and (8, 5)
Using the centroid formula, we can calculate the x-coordinate and y-coordinate of the third vertex separately.
For the x-coordinate:
1 = (-7 + 8 + x) / 3
3 = 1 + x
x = 3 - 1
x = 2
For the y-coordinate:
3 = (6 + 5 + y) / 3
9 = 11 + y
y = 9 - 11
y = -2
Therefore, the coordinates of the third vertex are (2, -2).