Questions on Geometry: Length, distance, coordinates, metric length answered by real tutors!

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Question 166150: Show that the points (4,5),(1,1) and (-2,5) are the vertices of an isosceles triangle. Find the area.: Show that the points (4,5),(1,1) and (-2,5) are the vertices of an isosceles triangle. Find the area.
Answer by MRperkins(77) About Me  (Show Source):
You can put this solution on YOUR website!
use the distance formulad=sqrt((x2-x1)^2+(y2-y1)^2)
find the distance between (4,5) and (1,1) distance=5
find the distance between (1,1) and (-2,5) distance=5
find the distance between (-2,5) and (4,5) distance=6
a triangle with 2 congruent sides is an isosceles triangle
next, bisect the angle where the two congruent sides meet and draw a straight line forming a 90 degree angle with the third side.
the new triangle that this forms has one side with length of 3, hypotenuse of 5 and an unknown length. Use the Pythagorean Theorum A^2+B^2=C^2 to find the 3rd side. We find that it is 4.
Then use the A=1/2BH formula to find the area of the triangle.
click on my name to go to my website, once there go to the "Solutions" page and there is a pdf file so you can see how this looks when drawn out.
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Hope this helps!
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MRperkins