Answer:see the explanationStep-by-step explanation:we know thatAn isosceles triangle has two equal sidesstep 1Find 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 2Find the length side AXthe formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we haveA(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 3Find the length side BXthe formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we haveB(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 4Compare the length side AX and BX[tex]AX=a\sqrt{2}\ units[/tex]
[tex]BX=a\sqrt{2}\ units[/tex]
[tex]AX=BX[/tex]soThe triangle AXB has two equal sidesthereforeTriangle AXB is an isosceles triangle