Answer: The orthocenter of triangle DEF is (-1,-4).
Step-by-step explanation:
The vertices of the triangle DEF are D(-1,2), E(-1,-4), F(2,-4).
Plot these pint on a coordinate plane as shown below.
From the figure we can conclude that the triangle DEF is an right angle triangle.
In a right angle triangle two legs are perpendicular to each other, It means both forms altitudes. So, the vertx at which contain the right angle is the orthocenter of the triangle.
From the figure it is noticed that the right angle is formed on E(-1,-4), therefore the orthocenter of the triangle DEF is (-1,-4).