Question

Assertion: The coordinates of the vertices of a triangle are (1, 1), (2, 5), and (3, 0). The coordinates of its centroid are (1, 2).

Reason: The coordinates of the centroid of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) are `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`.

Options

• Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Assertion (A) is false, but Reason (R) is true.

Explanation:

⇒ Using the centroid formula:

`((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`,

Here,

x = `(1 + 2 + 3)/3` = 2 and

y = `(1 + 5 + 0)/3` = 2,

So, the centroid is (2, 2), not (1, 2).

⇒ Thus, the assertion is false while the reason, which is the formula, is true.