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

answer: 38.47 is your answer

step-by-step explanation: hope i you and who ever sees this answer have a great rest of your day : )

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for