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Solution


Q.

Assertion (A): If the co-ordinates of the mid-points of the sides AB and AC of ΔABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units

Reason (R) : The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.
1 Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)  
2 Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)  
3 Assertion (A) is true but reason (R) is false.  
4 Assertion (A) is false but reason (R) is true.  

Ans.

(1)

For assertion : Distance between two points (x1,y1) and (x2,y2) =(x2-x1)2+(y2-y1)2

∴ Distance between DE=(-3-3)2+(-3-5)2

                                          =36+64=100=10 units

By midpoint theorem, distance between BC =2×distance between DE=2×10=20 units.

So, assertion is true.

For reason: By midpoint theorem, the line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it. So, reason is also true.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)