Question 20 Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC of ∆ABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units Statement R( Reason): The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason(R) is false. (d) Assertion (A) is false but reason(R) is true.Checking Assertion
Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC of ∆ABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units
We need to use the theorem in Reasoning
The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.
DE = 1/2BC
2DE = BC
BC = 2DE
BC = 2 × √((−𝟑−𝟑)^𝟐+(−𝟑−𝟓)^𝟐 )
BC = 2 × √((−6)^2+(−8)^2 )
BC = 2 × √(6^2+8^2 )
BC = 2 × √(36+64)
BC = 2 × √𝟏𝟎𝟎
BC = 2 × 10
BC = 20 cm
Thus, Assertion is true
Checking Reason
Statement R( Reason): The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.
This is always true
Here is a proof
https://www.teachoo.com/1660/518/Ex-6.2--8---Prove-that-line-joining-mid-points-of-any-two/category/Ex-6.2/
Thus, Reasoning is true
Is Reason a Correct explanation for Assertion?
Since we used Reasoning to explain Assertion
Therefore, Reasoning is a correct explanation for Assertion
So,
Assertion is true
Reasoning is true
But, Reasoning is a correct explanation for Assertion
So, the correct answer is (a)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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