Answer:
see the explanation
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides
step 1
Find the coordinates of point X (midpoint of segment AC)
we have
A(0,2a), C(2a,0)
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]X(\frac{0+2a}{2},\frac{2a+0}{2})[/tex]
[tex]X(a,a)[/tex]
step 2
Find the length side AX
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,2a), X(a,a)
substitute
[tex]AX=\sqrt{(a-2a)^{2}+(a-0)^{2}}[/tex]
[tex]AX=\sqrt{(-a)^{2}+(a)^{2}}[/tex]
[tex]AX=a\sqrt{2}\ units[/tex]
step 3
Find the length side BX
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
B(0,0), X(a,a)
substitute
[tex]BX=\sqrt{(a-0)^{2}+(a-0)^{2}}[/tex]
[tex]BX=\sqrt{(a)^{2}+(a)^{2}}[/tex]
[tex]BX=a\sqrt{2}\ units[/tex]
step 4
Compare the length side AX and BX
[tex]AX=a\sqrt{2}\ units[/tex]
[tex]BX=a\sqrt{2}\ units[/tex]
[tex]AX=BX[/tex]
so
The triangle AXB has two equal sides
therefore
Triangle AXB is an isosceles triangle
