Question

Q(-6,8), T(7,7), and R(-3,-5).

a. Identify the midpoint of QT
b. Calculate the slope of TR
c. Find the distance between points Q and R
d. Determine the quadrant in which point T lies

Answer 1

a. The midpoint of QT is [1/2, 15/2]. b. The slope of TR is 6/5. c. The distance between points Q and R is sqrt(178). d. Point T lies in Quadrant I.

Step-by-step explanation:

a. Midpoint of QT:

To find the midpoint of a line segment, we can use the midpoint formula:

Midpoint = [(x1 + x2) / 2, (y1 + y2) / 2]

Using the given coordinates, the midpoint of QT is:

[(7 + (-6)) / 2, (7 + 8) / 2] = [1/2, 15/2]

b. Slope of TR:

The slope of a line can be found by using the formula:

Slope = (y2 - y1) / (x2 - x1)

Using the coordinates of points T and R, we can calculate the slope of TR:

Slope = (-5 - 7) / (-3 - 7) = -12 / -10 = 6/5

c. Distance between points Q and R:

The distance between two points can be calculated using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given coordinates, the distance between points Q and R is:

Distance = sqrt((-3 - (-6))^2 + (-5 - 8)^2) = sqrt(9 + 169) = sqrt(178)

d. Quadrant in which point T lies:

Since the x-coordinate of point T is positive (7), and the y-coordinate of point T is positive (7), point T lies in Quadrant I.