Assertion Reasoning Quiz

Question 1 of 6

Assertion: The midpoint of \(A(-2,5)\) and \(B(6,-1)\) is \(M(2,2)\).
Reason: The midpoint is obtained by adding the corresponding coordinates of the endpoints without dividing by \(2\).

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 2 of 6

Assertion (A): The distance between the points \(A(-3, 2)\) and \(B(5, 2)\) is \(8\) units.
Reason (R): The distance between points \((x_1, y)\) and \((x_2, y)\) is calculated as \(|x_2 - x_1|\).

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is NOT the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

Select one option. Answers are shown after the test.

Question 3 of 6

Assertion (A): The perimeter of a triangle with vertices at \((0,0)\), \((3,0)\), and \((0,4)\) is \(12\) units.
Reason (R): The distance between \((3,0)\) and \((0,4)\) is calculated as \(5\) units using the Baudhāyana-Pythagoras theorem.

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is NOT the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

Select one option. Answers are shown after the test.

Question 4 of 6

Assertion (A): The image of the point \((3, -4)\) when reflected across the x-axis is \((3, 4)\).
Reason (R): When a point is reflected across the x-axis, its x-coordinate remains the same but the sign of its y-coordinate changes.

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is NOT the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

Select one option. Answers are shown after the test.

Question 5 of 6

Assertion (A): The distance between the points \(P(-1, -1)\) and \(Q(2, 3)\) is \(5\) units.
Reason (R): The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

A Both (A) and (R) are true, and (R) is the correct explanation of (A). B Both (A) and (R) are true, but (R) is NOT the correct explanation of (A). C (A) is true, but (R) is false. D (A) is false, but (R) is true.

Select one option. Answers are shown after the test.

Question 6 of 6

Assertion: The distance between two points changes when the order of the points is reversed.
Reason: In the distance formula, the coordinate differences are squared, so their signs do not affect the result.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

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