Question

HELP ASAP The points A(4, 0) and B(3, 7) are two vertices of right triangle ABC . The hypotenuse of the triangle is AB¯¯¯¯¯ . Point C is on the x-axis What are the coordinates of point C? Enter your answers in the boxes.

Answer 1

$\text{Answer: The coordinates of C is }(3,0)$

Explanation:

Since we have given that

A(4,0) and B(3,7) are two vertices of right triangle ABC.

The hypotenuse of the triangle is AB.

Construct a rectangle ABCD with AB as its diagonal ,

With the help of A(4,0) and B(3,7) we can find the coordinate of C ,

Since the x-coordinate of A and C will be same and the y-coordinate of B and C will be same ,

So, the coordinate of C becomes (3,0).

Similarly,

Since the x-coordinate of B and D and the y-coordinate of A and D will be same,

$\text{So, the coordinates of D becomes (4,7) }$

But From C and D we will choose  C as the third coordinate of Triangle because point C is on the x-axis.

$\text{Hence, the coordinates of C is (3,0)}$

Answer 2

If you draw a simple diagram you can see that point to form a right angle ACB, C must be at (3,0).