KnowledgeBoat Logo
|

Mathematics

Assertion (A): If the points A(2, 9), B(2, 5) and C(5, 5) are joined, then ΔABC is right angled.

Reason (R): If AC2 = AB2 + BC2, then ∠B = 90°.

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

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

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Coordinate Geometry

3 Likes

Answer

Given, the points A(2, 9), B(2, 5) and C(5, 5).

By distance formula,

Distance between two points = (x2−x1)2+(y2−y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

Given, points A(2, 9), B(2, 5) and C(5, 5).

Distance between AB =(2−2)2+(5−9)2=0+(−4)2=0+16=16=4 units.Distance between BC =(5−2)2+(5−5)2=32+02=9+0=9=3 units.Distance between AC =(5−2)2+(5−9)2=32+(−4)2=9+16=25=5 units.\text{Distance between AB }= \sqrt{(2 - 2)^2 + (5 - 9)^2} \\[1em] = \sqrt{0 + (-4)^2} \\[1em] = \sqrt{0 + 16} \\[1em] = \sqrt{16} \\[1em] = \text{4 units}. \\[1em] \text{Distance between BC } = \sqrt{(5 - 2)^2 + (5 - 5)^2} \\[1em] = \sqrt{3^2 + 0^2} \\[1em] = \sqrt{9 + 0} \\[1em] = \sqrt{9} \\[1em] = \text{3 units}. \\[1em] \text{Distance between AC } = \sqrt{(5 - 2)^2 + (5 - 9)^2} \\[1em] = \sqrt{3^2 + (-4)^2} \\[1em] = \sqrt{9 + 16} \\[1em] = \sqrt{25} \\[1em] = \text{5 units}.

AC2 = 52 = 25 units

AB2 = 42 = 16 units

BC2 = 32 = 9 units

Since, AC2 = AB2 + BC2, thus it satisfies pythagoras theorem.

Thus, ABC is a right angled triangle at B.

Thus, Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

Answered By

1 Like

Related Questions