How do you find the midpoint of the line segment with endpoints (sqrt50,1) and (sqrt2,- 1)?

2 Answers
Nityananda
Dec 17, 2016

(3sqrt2,0)

Explanation:

If the end points are (x_1, y_1) and (x_2, y_2)

then the midpoint is = [x_1 + x_2]/2, [y_1 + y_2}/2

Here (x_1,y_1) = (sqrt50, 1) and (x_2,y_2) = (sqrt2 , -1)

So midpoint = [sqrt50 + sqrt2]/2, [1 +(-1)]/2

or, [sqrt(5*5*2) +sqrt2]/2, [1 - 1]/2

or, [5sqrt2 + sqrt2]/2, 0/2

or,[sqrt2(5+1)]/2, 0

or, [6sqrt2]/2, 0

or, 3sqrt2, 0

Tony B
Dec 17, 2016

Mid point P_("mean") ->(x_("mean"),y_("mean"))=(3sqrt(2),0)

Explanation:

The mid point is the mean values

Let point 1 be P_1=(x_1,y_1) = (sqrt(50),1)
Let point 2 be P_2=(x_2,y_2)=(sqrt(2),-1))

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider x_1 = sqrt(50)

Note that 2xx25=50 but 25=5^2 so we have:

x_1=sqrt(2xx5^2) = 5sqrt(2)

Thus P_1->(x_1,y_1)=(5sqrt(2),1)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Determine the mean values")

x_("mean") ->barx = (5sqrt(2)+sqrt(2))/2= 3sqrt(2)

y_("mean")->bary = (1-1)/2=0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mid point P_("mean") ->(x_("mean"),y_("mean"))=(3sqrt(2),0)

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