HELP: Show that the points (4,5),(1,1) and (-2,5) are the vertices of an isosceles triangle. Find the Area.?

Question

Subject: Calculus with Analytical Geometry

Answer 1

Call the points A (4,5) B (1,1) and C (-2,5)
Calculate the distance from A to B and from B to C
If these distances are the same you have an isosceles triangle. (they will be).
The perpendicular bisector of A,C passes through (1,5) and (1,1) . Therefore the height of the triangle is 4 units. The base is 6 units.

Now you calculate the area.

Answer 2

in case you recognize the gap formula in 2-dimesions.....d=sqrt[(X2-X1)^2+(Y2-Y... merely boost it to 3 dimensions........d=sqrt[(X2-X1)^2+(Y2-Y... PQ:::d=sqrt9=3 PR:::d=sqrt2 QR:::d=sqrt9=3 Triangle is isosceles