The area of a right triangle can be found using the formula
`A = 1/2 ab` , where a and b are the lengths of the sides that form the right angle. This is an application of a more general formula for the area of any triangle: Area = 1/2*height*base.
By considering the coordinates of the vertices of the given triangle, we can notice that the y-coordinates of points A and B are the same (both are 0.) This means the segment AB is horizontal. The length of AB is then the difference of x-coordinates of points A and B: 7 - 1 = 6.
Also, the x-coordinates of points A and C are the same (both are 1.) This means the segment AC is vertical and its length is the difference of the y-coordinates of points A and C: 8 - 0 = 8.
Since the horizontal and vertical lines are perpendicular, AB and AC are perpendicular and form a right angle. Then the area of the right triangle ABC can be found as
`1/2* AB*AC = 1/2*6*8 = 24` .
The area of the given right triangle is 24.