The piece of graph paper is folded once so that (0,2) is matched with (0,-4) and (7,3 ) is matched with with (m,n).
Find (m+n).
Explain in detail.
Answers
Answer:
Required value of m + n is 2.
Step-by-step explanation:
Given diagrams are enough to explain the solution.
According to question, paper is folded in such a manner so that the points ( 0 , 2 ) is matched ( 0 , - 4 ). Since both the points are on y axis, we can say that the graph is folded along the y axis. And the mid point of ( 0 , 2 ) and ( 0 , - 4 ) i.e. ( 0 , - 1 ) should be located at the curve( end from where the paper is folded ).
Therefore,
Mid point of ( 7 , 3 ) and ( m , n ) should be perpendicular to ( 0 , - 1 ) in the direction of positive x axis and thus it must have - 1 in its y coordinate, and since paper is folded in the parallel direction of y axis, x coordinate of mid point should have 7. Hence, mid point of ( 7 , 3 ) and ( m , n ) is ( 7 , - 1 ).
So, by mid point formula,
= > ( 7 + m ) / 2 = 7 ⇒ 7 + m = 14 ⇒ m = 7
= > ( 3 + n ) / 2 = - 1 ⇒ 3 + n = - 2 ⇒ n = - 5
Then,
= > m + n = 7 + ( - 5 ) = 7 - 5 = 2
Hence the required value of m + n is 2.
Answer:
Step-by-step explanation:
