JoseMargareth0194idn
Answered

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If the mid-point between the points (a+b,a−b) and (−a,b) lies on the line ax+by=k , find k?

Please need ko po to​

Sagot :

EnterFreeidn

Answer:

The value of k is equal to ab

Step-by-step explanation:

Use the midpoint formula between two points:

                 [tex]\displaystyle (x_m,y_m)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]

Therefore, the midpoint between (a+b, a-b) and (-a, b) is

                [tex]\displaystyle \left(\frac{a+b-a}{2},\frac{a-b+b}{2}\right)=\left(\frac{b}{2},\frac{a}{2}\right)[/tex]

Next, we will use a fact:

  • If a point (p, q) lies on a line ax+by = c, then plugging (p, q) = (x, y) to the equation will give us a true equation.

Because the midpoint (b/2, a/2) lies on ax+by = k, plugging (b/2, a/2) = (x, y) to ax+by = k shall give us a true equation. Plug in (b/2, a/2) = (x, y):

           [tex]\displaystyle ax+by=a\left(\frac{b}{2}\right)+b\left(\frac{a}{2}\right)=\frac{2ab}{2}=ab=k[/tex]

So the value of k is equivalent to ab.