Final answer:
To find the area of the triangle formed by two points on a given line, we find the equation of the line passing through the origin and the midpoint of the line segment connecting the two points. Then, we find the point of intersection of this line with the given line. Using Heron's formula, we can calculate the area of the triangle by using the lengths of the sides.
Step-by-step explanation:
Given two points P and Q on the line x-y+1=0 which are at a distance of 5 units from the origin, we can find the equation of the line passing through the origin and the midpoint of the line segment PQ. Using the equation of the line, we can find the point of intersection with the given line x-y+1=0, let's call it R. Now, we have formed a triangle PQR. To find the area of this triangle, we can use the formula for the area of a triangle given three side lengths using Heron's formula:
Area = sqrt(s(s-a)(s-b)(s-c))
Where a, b, and c are the side lengths of the triangle, and s is the semi-perimeter given by s = (a+b+c)/2.