Question

QP had midpoint R. If Q is the point (-3,7) and P is the point (3, -1), what is the length of QR?

Answer 1

QR = 5 units

Step-by-step explanation:

The formula for calculating midpoint is expressed as;

R(X, Y) = {(x2+x1)/2, (y2+y1)/2}

X = x1+x2/2

Y = y1+y2/2

Given the follwing coordinates

Q (-3,7) and P (3, -1),

Get the midpoint R

R (X, Y) = (-3+3/2, 7-1/2)

R (X, Y) = (0/2, 6/2)

R (X, Y) = (0, 3)

Hence the midpoint R is (0,3)

Get the length of QR using the formula for calculating the distance between two points

`QR\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Given the coordinates Q(-3, 7) and R(0,3)

`\begin{gathered} QR\text{ = }\sqrt[]{(0-(-3))^2+(3-7)^2} \\ QR\text{ = }\sqrt[]{3^2+(-4)^2} \\ QR\text{ = }\sqrt[]{9+16} \\ QR\text{ = }\sqrt[]{25} \\ QR\text{ = 5} \end{gathered}`

Hence the length of QR is 5 units