Your answer is roughly 4.92 units, or √24.25 .
To find the length of line PQ, we need the coordinates of P and Q, and then we can use Pythagoras's theorem to find the distance between them. Because we know that PQ is a midsegment of triangle ABC, and also that it's parallel to BC, the coordinates of P and Q must be the midpoints of the lines AB and AC in the triangle.
To find a midpoint of a line, you add up the x coordinates and then half the result, and then add up the y coordinates and half the result. This means the midpoint of line AB is ( (8+1)/2, (6+1)/2 )= (4.5, 3.5). We can then label this point Q.
The midpoint of line AC is therefore ( (8+10)/2, (6-3)/2) = (9, 1.5). We can label this point Q.
Now to find the length of PQ, we can use Pythagoras's theorem. First we need to find the difference between the x coordinates and y coordinates of P and Q to be the legs of the right-angled triangle. These will be (9 - 4.5) = 4.5 for the base, and (3.5 - 1.5) = 2 for the height.
Thus, the length of PQ is √(2² + 4.5²) = √(4 + 20.25) = √24.25 . This is roughly equal to 4.92.
I hope this helps! Let me know if you have any questions :)
