Advertisements
Advertisements
Question
Find the Y-coordinate of the centroid of a triangle whose vertices are (4, –3), (7, 5) and (–2, 1).
Solution
Vertices of a triangle,
(4, –3), (7, 5) and (–2, 1) .....[Given]
x1 = 4, Xz = 7, x3 = –2
y1 = –3, y2 = 5, y3 = 1
By using the centroid formula,
`[(x_1 + x_2 + x_3)/3, ("y"_1 + "y"_2 + "y"_3)/3]` = coordiante of centroid
Now, Y-coordinate of centroid = `[("y"_1 + "y"_2 + "y"_3)/3]`
= `(-3 + 5 + 1)/3`
= `3/3`
= 1
∴ Y-coordinate of centroid = 1.
APPEARS IN
RELATED QUESTIONS
Find the centroid of the triangle whose vertice is given below.
(–7, 6), (2, –2), (8, 5)
Find the centroid of the triangle whose vertice is given below.
(3, –5), (4, 3), (11, –4)
Find the centroid of the triangle whose vertice is given below.
(4, 7), (8, 4), (7, 11)
In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.
In the following example, can the segment joining the given point form a triangle? If triangle is formed, state the type of the triangle considering side of the triangle.
P(–2, –6) , Q(–4, –2), R(–5, 0)
In the following example, can the segment joining the given points form a triangle? If triangle is formed, state the type of the triangle considering sides of the triangle.
A(√2, √2), B(−√2, −√2), C(−√6, √6)
Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5).
Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle.
LMNP is a parallelogram. From the information given in the figure fill in the following boxes.
MN = cm
PN = cm
∠ M =
∠ N =
Find the coordinates of centroid of a triangle whose vertices are (4, 7), (8, 4) and (7, 11)
The coordinates of the vertices of a triangle ABC are A (–7, 6), B(2, –2) and C(8, 5). Find coordinates of its centroid.
Solution: Suppose A(x1, y1) and B(x2, y2) and C(x3, y3)
x1 = –7, y1 = 6 and x2 = 2, y2 = –2 and x3 = 8, y3 = 5
Using Centroid formula
∴ Coordinates of the centroid of a traingle
ABC = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`
= `(square/3, square/3)`
∴ Coordinates of the centroid of a triangle ABC = `(3/3, square)`
∴ Coordinates of the centroid of a triangle ABC = `(1 , square)`
The points (7, – 6), (2, k) and (h, 18) are the vertices of triangle. If (1, 5) are the coordinates of centroid, find the value of h and k
Find the centroid of the ΔABC whose vertices are A(–2, 0), B(7, –3) and C(6, 2).
