Question

5.) If A (-14, -19), B (3,5) and C (-1, -7) are the vertices of A ABC then its
centroid is
O (
(-2,-5)
0 (-5, -8)
0 (-3,-5)
W
0 (-4,-7)​

Answer 1

QUESTION :

If A (-14, -19), B (3,5) and C (-1, -7) are the vertices of triangle ABC then its centroid is -

(A) (-2,-5)

(B) (-5, -8)

(C) (-3,-5)

(D) (-4,-7)

SOLUTION :

Given :

A (-14, -19), B (3,5) and C (-1, -7) are the vertices of the triangle. (refer figure)

TO FIND :

centroid of given triangle.

Concept and Formula Used :

⚫The centroid of triangle (any triangle- isosceles, scalene or equilateral )is the intersection of the 3 medians of the triangle.

⚫Formula of centroid =>

Let the Centroid be at point C with coordinates = x and y.

Therefore :-

$x = \frac{a+ b + c}{3}$

$y = \frac{l + m + n}{3}$

where => (a,l) , (b,m) and (c,n) are vertices of triangle.

Procedure :

we have , vertices given as =>

A (-14, -19), B (3,5) and C (-1, -7)

To find the Centroid of given triangle :-

we will use the FORMULA :-

$x= \frac{a+ b + c}{3}$

$y = \frac{l + m + n}{3}$

Now to find the coordinates of centroid put the given values in the formula.

Therefore :-

→$x= \frac{ - 14+ 3 + ( - 1)}{3}$

→$x= \frac{ - 14+ 3 - 1}{3}$

→$x= \frac{ - 15+ 3 }{3}$

→$x = \frac{ - 12}{3}$

→$x = - 4$

Therefore, x coordinate of centroid = -4

Now we will find y coordinate.

→$y = \frac{ - 19 + 5+( - 7)}{3}$

→$y = \frac{ - 19 + 5+( - 7)}{3}$

→$y = \frac{ - 26 + 5}{3}$

→$y = \frac{ - 21}{3}$

→$y = - 7$

Therefore, y coordinate of centroid = -7

Therefore , Centroid = (-4,-7)

ANSWER : option (D) is correct.

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⚫Learn More :-

⟹ Centroid of a triangle is the intersection of the 3 medians of triangle.

⟹ Median is a line that connects midpoint of one side and the opposite vertex of the triangle.

⟹Centroid divides median into the ratio 2:1.

⟹Centroid always lie inside figure or object.

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