If the centroid of a triangle formed by (4,x), (y,-5) and (7, 8) is (3

1.	If the centroid of a triangle formed by (4,x), (y,-5) and (7, 8) is (3, 5), then the values of x and y are respectively1. 2, 122. -12, 133. 12, -24. 13, -2
Answer» Correct Answer - Option 3 : 12, -2 Concept: The centroid of a Triangle: The point where the three medians of the triangle intersect. Let’s consider a triangle. If the three vertices of the triangle are A(x1, y1), B(x2, y2), C(x3, y3) The centroid of a triangle =\(\rm (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})\) Calculation: Here, vertices of triangle (4,x), (y,-5) and (7, 8) and Centroid = (3, 5) So, 3 = \(\rm \frac{4+y+7}{3}\) ⇒11+y = 9 ⇒ y = -2 And, 5 = \(\rm \frac{x-5+8}{3}\) ⇒ x + 3 = 15 ⇒ x = 12 ∴ x = 12, and y = -2 Hence, option (3) is correct.

If the centroid of a triangle formed by (4,x), (y,-5) and (7, 8) is (3, 5), then the values of x and y are respectively1. 2, 122. -12, 133. 12, -24. 13, -2

Answer» Correct Answer - Option 3 : 12, -2

Concept:

The centroid of a Triangle: The point where the three medians of the triangle intersect.

Let’s consider a triangle. If the three vertices of the triangle are A(x1, y1), B(x2, y2), C(x3, y3)

The centroid of a triangle

=\(\rm (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})\)

Calculation:

Here, vertices of triangle (4,x), (y,-5) and (7, 8) and Centroid = (3, 5)

So, 3 = \(\rm \frac{4+y+7}{3}\)

⇒11+y = 9

⇒ y = -2

And, 5 = \(\rm \frac{x-5+8}{3}\)

⇒ x + 3 = 15

⇒ x = 12

∴ x = 12, and y = -2

Hence, option (3) is correct.