Notice that $△ Z Y C$ is a right triangle as well as an isosceles triangle and that $Z Y = Y C .$

Since $Y$ is on the $x -$ axis, its $y -$ coordinate is $0 .$ Additionally, because $C$ is on a vertical segment that passes through $Y,$ we know that its $x -$ coordinate is $a .$

Finally, since $Z Y = Y C$ and $Z Y = a,$ it must be that $Y C = a .$ Therefore, the $y -$ coordinate of $C$ is $a .$

Extra

Types of Triangles

More information about the other types of triangles can be found in the following table.

Classification of Triangles
Scalene Triangle	A scalene triangle is a triangle in which all three sides have different lengths.
Isosceles Triangle	An isosceles triangle is a triangle that has two congruent sides and two base angles with the same measure.
Equilateral Triangle	An equilateral triangle is a triangle in which all the sides are congruent.
Acute Triangle	An acute triangle is a triangle where all angles are less than $9 0^{\circ}$ or $\frac{π}{2} .$
Obtuse Triangle	An obtuse triangle is a triangle with exactly one an angle whose measure is greater than $9 0^{\circ}$ or $\frac{π}{2} .$
Right Triangle	A right triangle is a specific type of triangle that contains one angle of $9 0^{\circ} .$

Exercise