The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2). On a coordinate plane, line A B has points (4, 1) and (negative 1, negative 2). At which points could the vertex of the right angle in the triangle be located? Check all that apply. (–1, 1) (4, –2) (1, 1) (2, –2) (4, –1) (–1, 4)

Step-by-step explanation:

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

To find: coordinates of vertex of the right angle

Solution:

Let C be point

Distance between points is given by

ΔABC is a right angled triangle, suing Pythagoras theorem (square of hypotenuse is equal to sum of squares of base and perpendicular)

Put

which is true. So, can be a vertex

Put

which is true. So, can be a vertex

Put

which is not true. So, cannot be a vertex

Put

which is not true. So, cannot be a vertex

Put

which is not true. So, cannot be a vertex

Put

which is not true. So, cannot be a vertex

So, possible points for the vertex are

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation: