The best step to start will be step D as in the rest of the options we do not know the coordinates of all three points.
If we start with Step A, we are unknown about points Q and R and these two points need to be located somewhere.
If we start with step B, we are unknown about point Q and it needs to be located.
If we start with step C, we are unknown about points P and R, and these two points need to be located.
Let us start with step D,
It is given that,
In triangle PQR, QR lies on the x-axis while PQ lies on the y-axis means Q will be at the origin
Coordinates of Q will be (0,0)
Let us take coordinates of R (4,0) and P as (0,4)
Let us take the midpoints of PQ &PR as ‘S’ & ‘T’ respectively.
Now, coordinates of S and T can be found using the Mid-Point formula
Coordinates of mid-point = (x1+x2)/2, (y1+y2)/2
Coordinates of S= (2,0)
Coordinates of T= (2,2)
WHAT IS THE MID-POINT THEOREM?
In a triangle, when midpoints of any two sides are joined, the line joining these points is half as well as parallel to the third side.
So, we have to prove ST= QR/2 and ST Parallel to QR.
(1) Now, using distance formula,
ST = √([(0-2)^2+(2-2)^2 ] )
ST = 2 (half of QR)
(2) Now, in order to prove ST is parallel to QR, we need to prove that the slope of ST is equal to the slope of QR.
Using slope formulae
Slope of ST = (2-2)/(2-0) = 0
Slope of QR = 0, as we know slope of x-axis is 0.
So, the value of ST is half of QR as well as it is parallel to QR.
Therefore, step D is the best option to start with.
To get more about the mid-point theorem refer to the link,
https://brainly.com/question/9635025
