Question

Evan drew a triangle which has an area of 4 sq.units. The two vertices of the triangle are (2,8) and (4,−4) and the third vertex with coordinate (x1,y1) lies on the line y=x+1. Which one is the highest among the possible values of x1+y1?

Answer 1

To find the maximum x1 + y1, find the coordinates (x1, y1) based on the given conditions (two vertices and area of the triangle) and the fact that the vertex lies on the line y = x+1. Use the information given to make careful calculations.

Step-by-step explanation:

In order to determine the highest possible values of x1 + y1, we first need to determine the equation for the area of the triangle. The area of a triangle given the vertices can be computed using the formula of 1/2[{(x1y2 + x2y3 + x3y1) - (x2y1 + x3y2 + x1y3)}]. Given the two vertices are (2, 8) and (4, -4) and the area is 4, we have two possible coordinates for (x1, y1).

As a triangle must have positive area, to get maximum x1 + y1 value, we take the possible (x1, y1) that delivers positive area. The third vertex (x1, y1), is on line y = x+1. Hence, the pair x1 and y1 has to satisfy this line equation in other to retain triangle's area.

By using the information given and following these steps, you can determine the highest combination of x1 + y1. Remember to use precise and detailed calculations in order to get an accurate answer using the given vertices and the relationship between x1 and y1.

Learn more about Triangle Area