Given the vertices of a right triangle are A(1,0), B(7,0) and C(1,8), how would you find the area of the triangle?

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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.

 

 

 

 

 

 

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