Question

The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).

Answer 1

Answer:

(–1, 1)

(4, –2)

Step-by-step explanation:

Given that the hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2), then two triangles can be formed (see figure attached).

The vertex of the right angle in each triangle are on points (-1, 1) and (4, -2), as can be seen in the figure.

Answer 2

Answer:

(–1, 1)

(4, –2)

Step-by-step explanation:

Let

(x,y) ----> the coordinates of point C

Applying the Pythagoras Theorem

$(-1-4)^2+(-2-1)^2=(x-4)^2+(y-1)^2+(x+1)^2+(y+2)^2$

step 1

Find the possibles values of x

$(-1-4)^2=(x-4)^2+(x+1)^2\\\\25=x^{2}-8x+16+x^{2}+2x+1\\\\2x^{2}-6x-8=0$

Simplify

$x^{2}-3x-4=0$

Solve the quadratic equation

$x^{2}-3x-4=(x+1)(x-4)$

The values of x are

x=-1 and x=4

step 2

Find the possibles values of y

$(-2-1)^2=((y-1)^2+(y+2)^2\\\\9=y^{2}-2y+1+y^{2}+4y+4\\\\2y^{2}+2y-4=0$

Simplify

$y^{2}+y-2=0$

Solve the quadratic equation

$y^{2}+y-2=(y+2)(y-1)$

The values of y are

y=-2, y=1

therefore

The possibles coordinates of point C are

(-1,1),(4,-2)