Question

A textbook has a picture of a triangle with vertices (3,6) and (5,2). Something happened in printing the book and the coordinates of the third vertex are listed as (-1, ). The answers in the back of the book give the area of the triangle as 6 square units. What is the y-coordinate of this missing vertex?

Answer 1

To find the missing y-coordinate, we apply the area formula for a triangle using the known vertices and solve the resulting equation. This yields the correct y-value that, alongside the other given vertex coordinates, results in a triangle with the area listed in the textbook.

Step-by-step explanation:

The problem involves finding the missing y-coordinate of the third vertex of a triangle with an area of 6 square units, where the first two vertices are given as (3,6) and (5,2), and the partial coordinates of the third vertex are (-1, y). The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by the absolute value of the formula:

A = (1/2) |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|

Given the area is 6, we can plug in the known values and solve for the missing y-coordinate:

6 = (1/2) |3(2-y) + 5(y-6) - 1(6-2)|

After simplifying the equation, you can find the correct value for y. The printing mistake did not affect the calculation, as the correct coordinates allow the computation of the right area for the triangle.