The vertices of a triangle are A(4, 1), B(9, 1), and C(2, 5). What is the area of this triangle?

Question

I need help with this problem\. I'm in 6th grade a straight A student and need your help. thanks alot

Answer 1

I don't know how much you have learned about coordinate geometry and the area of triangles, but if you plot the 3 points on the Cartesian plane and connect them with line segments you will see that they form an obtuse triangle. The area of a triangle is equal to (1/2) base times height. Let AB be the base of the triangle, it has length 5. The height of the triangle is the perpendicular distance from line AB to point C. Since AB is a horizontal line, its perpendicular will be a vertical line from the point (2,1) to point C at (2,5). (You need to extend line segment AB to the left to see this). This perpendicular distance is equal to 4, so the area of the triangle is equal to (1/2)*5*4 = 10.