Question

PLEASE ANSWER ASAP

Beverly is trying to prove that △PQR is a right triangle.

The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3). Which TWO slope calculations

can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.

Answer 1

Beverly can use the slopes of line segments PQ and QR to show that △PQR is a right triangle, as their slopes are negative reciprocals which prove perpendicularity.

Step-by-step explanation:

Beverly can prove that △PQR is a right triangle by calculating the slopes of two of the sides and showing that they are perpendicular by means of their slopes being negative reciprocals of each other. The slope of the line segment PQ can be calculated using the coordinates P(-2, 5) and Q(-1, 1), and the slope of the line segment QR can be calculated using the coordinates Q(-1,1) and R(7, 3).

The slope of PQ is found by the formula slope = (y2 - y1) / (x2 - x1), which gives us (1 - 5) / (-1 - (-2)) = -4 / 1 = -4. Similarly, the slope of QR is (3 - 1) / (7 - (-1)) = 2 / 8 = 1/4. Since the slopes are negative reciprocals (-4 and 1/4), this indicates that PQ and QR are perpendicular, thus confirming that △PQR is a right triangle.

Answer 2

Triangle PQR is a right triangle. First we have to find the length of each side of the triangle. This can be done using the points provided, along with the Pythagorean theorem, which is a^2+b^2=c^2. PR^2 = (7- -2)^2+(3-5)^2 = 85 => PR = sqrt(85) QR^2 = (7- -1)^2+(3-1)^2 = 68 => QR = sqrt(68) QP^2 = (1-5)^2+(-1 - -2)^2 =17 => QP = sqrt(17) Now that we have the sides of the triangle, we can put them into the Pythagorean theorem again to see that it works out: (Sqrt(17))^2 + (sqrt(68))^2 = (sqrt(85))^2 17 + 68 = 85 85 = 85 Since the Pythagorean theorem works for right triangles, the triangle is indeed a right triangle.

Step-by-step explanation: