 Hi, I am Kanika and I am going to help you to solve the following question. The question says the hypergenic use of a right-angled triangle has its nth at the points 1, 3 and minus 4, 1. Find the equation of the left's perpendicular sides of the triangle. Let's first take a figure of this question. Let ACB be a right-angled triangle at C. AB is the hypergenic use and this hypergenic use has its nth at the points 1, 3 and minus 4, 1. This means A has coordinates 1, 3 and B has coordinates minus 4, 1. We have to find the equation of left's. That means we have to find the equation of perpendicular sides AC and BC of this triangle. Let's now begin with the solution. Let ACB be the right-angled triangle at C, slope of AC. Slope of AC therefore minus 1 by n is the slope of BC perpendicular to BC and we know that product of slopes of two perpendicular is minus 1. Let's now find equation of AC. We know that equation of line passing through point x1, y1 and having slope m is y minus y1 is equal to m into x minus x1. Here line AC is passing through point 1, 3 and having slope m. So equation of AC is y minus 3 is equal to m into x minus 1 into y minus 3 is equal to x minus 1. Find equation of BC. Line BC is passing through point minus 4, 1 and having slope minus 1 by m. So equation of BC is y minus 1 is equal to minus 1 by m into x plus 4. Now as AC and BC are perpendicular to each other, therefore angle between these two sides is 90 degree. And we know that slope of a line is given by m is equal to tan theta. Now here theta is equal to pi by 2 so this means m is equal to infinity. So for m is equal to infinity, equation of AC reduces to x minus 1 is equal to 0 and equation of BC reduces to y minus 1 is equal to 0 and this implies x is equal to 1 and y is also equal to 1. Hence the required equation of perpendicular sides of the triangle are x is equal to 1 and y is equal to 1. This is our required answer.