Advertisements
Advertisements
Question
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
Advertisements
Solution
The given points are A(2,2) , B (-4,-4) and C (5,-8).
`Here , (x_1 = 2, y_1=2), (x_2=-4, y_2=-4) and (x_3=5 , y_3 =-8)`
Let G (x ,y) br the centroid of Δ ABC Then ,
`x= 1/3 (x_1+x_2+x_3)`
`=1/2(2-4+5)`
=1
`y=1/3(y_1+y_2+y_3)`
`=1/3 (2-4-8)`
`=(-10)/3`
Hence, the centroid of ΔABC is G `(1,(-10)/3).`
APPEARS IN
RELATED QUESTIONS
Prove that the points (−2, 5), (0, 1) and (2, −3) are collinear.
If G be the centroid of a triangle ABC, prove that:
AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)
The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, Show that PQRS is a rhombus.
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?
Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).
If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
Abscissa of a point is positive in ______.
Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.
