Question

a right triangle is formed in the first quadrant by the coordinate axes and a line segment passing through the point (2,3). Find the vertices of the triangle so that the area is a minimum.

Answer 1

To find the vertices of the triangle such that the area is a minimum, we need to consider the equation of the line passing through the point (2,3).

Step-by-step explanation:

To find the vertices of the triangle such that the area is a minimum, we need to consider the equation of the line passing through the point (2,3). Let's assume the equation of the line is y = mx + b, where m is the slope and b is the y-intercept.

Since this line passes through (2,3), we can substitute x = 2 and y = 3 into the equation to find the value of b.

Next, we find the x-intercept and the y-intercept of the line. The x-intercept is the point where the line intersects the x-axis, so we set y = 0 in the equation y = mx + b and calculate the corresponding value of x.

Similarly, the y-intercept is the point where the line intersects the y-axis, so we set x = 0 in the equation and calculate the corresponding value of y.

The vertices of the triangle can be found by using the x-intercept, the y-intercept, and the given point (2,3).