 Hi, and welcome to our session. Let us discuss the following question. The question says the line through the points h3 and 4 1 intersects line 7x minus 9y minus 19 is equal to 0 at right angle. Find the value of h. Let's now begin with the solution. In this question, we will first find the slope of line passing through points h3 and 4 1. Since this line intersects the line 7x minus 9y minus 19 is equal to 0 at right angle, therefore, by using the result, that product of slopes of two perpendicular lines is minus 1. We will find the value of h. So let's first find the slope of line passing through. We know that passing through points x1, y1, and x2, y2 is y2 minus y1 upon x2 minus x1. Now here, x1, y1 is h3, and x2, y2 is 4 1. So slope of line passing through h3 and 4 1 is 1 minus 3 upon 4 minus h. This is equal to minus 2 upon 4 minus h. So m1, that is slope of line passing through h3 and 4 1 is minus 2 by 4 minus h. Now we will find the slope of second line, that is 7x minus 9y minus 19 is equal to 0. Now 7x minus 9y minus 19 is equal to 0 implies minus 9y is equal to minus 7x plus 19. This implies y is equal to 7 by 9x minus 19 by 9. Now this equation is of the form y is equal to mx plus c. On comparing this equation with y is equal to mx plus c, we find that m is equal to 7 by 9. So slope of line 7x minus 9y minus 19 is equal to 0 is 7 by 9. So m2 is equal to 7 by 9. m1 into m2 is equal to minus 1 as lines are perpendicular. Now substitute the value of m1 and m2. m1 is equal to minus 2 by 4 minus h into m2 is 7 by 9. Now this implies minus 14 upon 4 minus h into 9 is equal to minus 1. This implies 14 upon 36 minus 9h is equal to 1. This implies 14 is equal to 36 minus 9h. This implies 9h is equal to 36 minus 14. This implies 9h is equal to 22. This implies h is equal to 22 by 9. Hence the required value of h is 22 by 9. This concludes the session. Bye and take care.