Answer-
The coordinates of the orthocenter of △JKL is (-4, 8)
Solution-
The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.
For a right angle triangle, the vertex at the right angle is the orthocentre of the triangle.
Here we are given the three vertices of the triangle are J(-4,-1), K(-4,8) and L(2,8)
If the triangle JKL satisfies Pythagoras Theorem, then triangle JKL will be a right angle triangle.
Applying distance formula we get,
[tex]JK^2= (-4+4)^2+ (8+1)^2=0+81=81\\\\KL^2= (-4-2)^2+ (8-8)^2=36+0=36\\\\JL^2= (-4-2)^2+(8+1)^2=36+81=117[/tex]
As,
[tex]\Rightarrow 117=81+36[/tex]
[tex]\Rightarrow JL^2=JK^2+KL^2[/tex]
[tex]\Rightarrow \text{JKL is a right angle triangle}[/tex]
[tex]\Rightarrow \angle K=90^{\circ}[/tex]
Therefore, the vertex at K (-4, 8) is the orthocentre.
