The endpoints of `bar(ef)` are e(xe , ye) and f(xf , yf). what are the coordinates of the midpoint of `bar(ef)`? a. `((x_f)/()/(2))` b. `((x_e)/()/(2))` c. `((x_e+x_f)/(+y_f)/(2))` d. `(x_e+(x_f)/(2),y_e+(y_f)/(2))`

For a better understanding of the solution provided here please find the diagram attached.

Please note that in coordinate geometry, the coordinates of the midpoint of a line segment is always the average of the coordinates of the endpoints of that line segment.

Thus, if, for example, the end coordinates of a line segment are and then the coordinates of the midpoint of this line segment will be the average of the coordinates of the two endpoints and thus, it will be:

Thus for our question the endpoints are and and hence the midpoint will be:

Thus, Option C is the correct option.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

answer: x=60