Four points are shown on a number line. the number –3 corresponds to the point a, −5 corresponds to point b, and 6 corresponds to point c. find the number that corresponds to the fourth point, k, in response to the following condition: if you will change the direction of the number line to the opposite, then the sum of the ‘new’ points that correspond to the ‘old’ points a, b, c, and k will not change. need asap

We are given:

A = - 3
B = - 5
C = 6
Let the Fourth point is x. Then
K = x

Sum of these points = -3 + (-5) + 6 + x = - 2 + x

When the direction of number line is changed to opposite, the signs of all the points will be changed.

So, now
A = 3
B = 5
C = -6
D = -x

The sum in this case is = 3 + 5 - 6 - x = 2 - x

It is given that the sum remains the same. So we can write:

-2 + x = 2 - x

x + x = 2 + 2

2x = 4

x = 2

We assumed x to be the Fourth point K. So the point K will be position 2 on the number line.

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