To find the equations of the sides of triangle DEF, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2).
Given that the midpoints are:
Midpoint of EF = P(6, 4)
Midpoint of FD = Q(5, 3) (Assuming you meant Q instead of R)
Midpoint of DE = R(3, 3)
Now, let's find the equations of the sides EF, FD, and DE.
For side EF, we have two endpoints, E and F. We can use the midpoint P(6, 4) to find one of the endpoints (let's say E):
Midpoint formula:
P(6, 4) = ((x_E + x_F)/2, (y_E + y_F)/2)
Substituting the values of P:
6 = (x_E + x_F)/2
4 = (y_E + y_F)/2
Now, you can use these equations along with the coordinates of P to solve for E. You will find that E is (4, 4).
So, the equation of side EF is the line passing through points E(4, 4) and F. You can use the point-slope formula to find it:
y - y1 = m(x - x1), where m is the slope.
Let's assume the slope is "m."
y - 4 = m(x - 4)
For side FD, you can follow a similar process using the midpoint Q(5, 3) and the known coordinates of F to find D.
For side DE, you can use the midpoint R(3, 3) and the known coordinates of D to find E.
Once you find the coordinates of the missing vertices (D and E), you can use them to write the equations of the sides FD and DE in a similar manner.