SOLUTION: show that the points (-3,1), (3, -1), (1,3) are the vertices of an isosceles triangle. Find its Area

Question 1008657: show that the points (-3,1), (3, -1), (1,3) are the vertices of an isosceles triangle. Find its Area
Answer by wynger566(1) (Show Source): You can put this solution on YOUR website!
Let, A(-3,1), B(3,-1) and C(1,3) be the given points.
Using distance formula;
d=√[(x2-x1)^2+(y2-y1)^2]�we get
AB=√40
BC=√20 units and
AC=√20 units
Clearly BC=AC. Hence, ABC is an isosceles triangle.
For area '
From C drop perpendicular to AB then
a name it as D
Using mid point formula;
we get D= (0,0)-------> origin
also length of CD is √10 units
Finally area=1/2 AB.CD=1/2 √40 .√10 =10 sq. units
RELATED QUESTIONS
show that the points(1,-3),(3,2),(-2,4) are the vertices of an isosceles triangle and... (answered by josgarithmetic,ikleyn)

show that the points (-3,1),(3,-1),(1,3) are the vertices of an isosceles triangle. find... (answered by Alan3354)

show that (-3, 1), (3, -1) and (1, 3) are the vertices of an isosceles triangle. find its (answered by mananth)

Show that the points (5,4), (-2,1) and (2,-3) are the vertices of an isosceles triangle,... (answered by Alan3354)

Show that the points A (3,-5), B (-3,-1) and C (7,1) are vertices of an isosceles... (answered by jim_thompson5910)

Show that the points (-2,4),(3,-1) and (-1,-3) are the verticles of an isosceles triangle (answered by Alan3354)

Show that the points R (-1 , 2), K (5 , 2) and O (2 , 5) are the vertices of an isosceles (answered by Alan3354)

show that the points(4,0),(2,1),(-1,-5) are the vertices of a right triangle and find its (answered by ikleyn)

Show that the points (4,5),(1,1) and (-2,5) are the vertices of an isosceles triangle.... (answered by MRperkins)