Math Is Fun Forum

Lolz

Member

Registered: 2017-07-30

Posts: 4

help! Geo

Plz give hints to the problem. It seems easy but it is not.

The points $A\, (5,-5)$ and $B\, (-1,-1)$ are the endpoints of the hypotenuse of an isosceles right triangle $\triangle ABC$. What is the area of $ABC$?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,634

Re: help! Geo

hi Lolz

welcome to the forum.

I think I can help.  Stay on -line while I make a diagram

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,634

Re: help! Geo

OK. Not quick enough to catch before you logged out.  Never mind I have it sorted.  If AB is the hypotenuse, and C is 90 degrees, there's a property of circles that AB is also a diameter.  The theory is here:

http://www.mathisfunforum.com/viewtopic.php?id=17799

see post 6

So draw coordinate axes, mark A and B and find the midpoint, O.  This is the centre of a circle that goes through A, B and C.  Draw a line at right angle to AB, through O to cut the circle at C.  From there it should be straight forward, but post back if you are still having difficulties.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: help! Geo

Do you visualize if hypotenuse is taken as base the height of the triangle equals half the length of hypotenuse?

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,634

Re: help! Geo

Can do, but I was thinking of doing 0.5 CB.CA

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Lolz

Member

Registered: 2017-07-30

Posts: 4

Re: help! Geo

Or we could use something like trig, but we don't have the angles to do it fast. Anyway, the midpoint between the two lines is (4,-3). It would be nice if there was an online calculator... but didn't find one. Is there a formula for this problem?

I was working on this problem mentally and got something...probably wrong.

Last edited by Lolz (2017-07-30 06:49:45)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: help! Geo

In a right angle triangle the vertices are on a circle with hypotenuse as diameter.The segment joining midpoint of hypotenuse to the opposite vertex is a radius. If the triangle is also isosceles this segment is perpendicular to the hypotenuse. So the area of the triangle is=1/2*hypotenuse *(hypotenuse/2).

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Lolz

Member

Registered: 2017-07-30

Posts: 4

Re: help! Geo

all I did wuz take 30 seconds to think really hard on it and got it. Answer is 13.

Last edited by zetafunc (2017-07-31 21:13:14)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: help! Geo

Nice.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}