If the centroid of the triangle with vertices | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The centroid $(G)$ of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by the formula: $G = (\frac{x_1 + x_2 + x_3}{3}

Vedclass · Accepted Answer

$a = 2, b = -5$

Vedclass · Answer

(A) The centroid $(G)$ of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by the formula: $G = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})$.Given vertices are $(-5, 3), (a, -1),$ and $(6, b)$,and the centroid is $(1, -1)$.Equating the $x$-coordinates: $\frac{-5 + a + 6}{3} = 1 \implies a + 1 = 3 \implies a = 2$.Equating the $y$-coordinates: $\frac{3 - 1 + b}{3} = -1 \implies 2 + b = -3 \implies b = -5$.Therefore,the values are $a = 2$ and $b = -5$.

If the centroid of the triangle with vertices $(-5, 3), (a, -1), (6, b)$ is $(1, -1)$,then find the values of $a$ and $b$.

Similar Questions

In which ratio does the point $P (2, b)$ divide the line segment joining $A (1, 2)$ and $B (4, 5)$ from $A$? Also,find the value of $b$.

Two vertices of a triangle are $A(2, 1)$ and $B(3, -2)$. The third vertex is $C(x, y)$,where $y = x + 3$. If the area of the triangle is $5$,find the coordinates of the third vertex.

Find $k$ if $(1, 7), (2, 4)$ and $(k, 5)$ form a right triangle.

If $A(3, 5)$ and $B(7, 5)$,then the midpoint of $\overline{AB}$ is $\ldots \ldots \ldots \ldots .$

Show that $(10, -18), (3, 6)$ and $(-5, 2)$ are the vertices of an isosceles triangle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module