Plan: place the right triangle in the coordinate plane with the vertex of the (a) at the origin and the (b) along each axis. since midpoints will be involved, use (c) to name the coordinates for points m and n. use the (d) formula to find the coordinates of p. to compare lengths, use the (e) formula. select the best phrase to enter in place of blank (b) in the above plan. a. multiples of 2 b. midpoint c. legs d. right angle

Legs

Plan: Place the right triangle in the coordinate plane with the vertex of the (a) at the origin and the (b) along each axis.

Question says place the right angle in the coordinate plane.

It is a right angle triangle. If we place a right angle vertex at the origin then other two sides will be along x axis and y axis.

Place the right triangle in the coordinate plane with the vertex of the right angle at the origin and the legs along each axis.

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).