Wednesday

October 22, 2014

October 22, 2014

Posted by **Emily** on Sunday, October 23, 2011 at 6:16pm.

- geometry -
**bobpursley**, Sunday, October 23, 2011 at 6:33pmThe C willbe on the line which is the perpendicular bisector of the hypotenuse.

slope of AB= (6/-4)

slope of bisector= 4/6

but a point on the bisector is (6,4)

y= 4/6 x + b

4= 4/6 *6+b

B=0

equation of bisector is y= 4/6 x

now, there is a point on that line which forms to line segments which are 90 deg to each other.

C (x,y)=(x,4/6x)

Now, if AC and BC are perpendicular the slopes are neg reciprocals.

slope AC= (7-4x/6)/(4-x)

slope BC= (8-4x/6)/(1-x)

these are neg reciprocals, so this leads to

(7-4x/6)(8-4x/6)=-(4-x)(1-x)

solve for x. It looks a little messy.

56-8x/6+16x^2/36=-4+5x-x^2

combine terms, simplify, solve for x with the binomial equation.

**Answer this Question**

**Related Questions**

Geometry - The coordinates of the endpoints of the hypotenuse of a right ...

Math(Geometry) - In the diagram below(no diagram but details will be provided), ...

Math (Geometry) - The perimeter of right triangle ABC is equal to the perimeter ...

Math - the right triangle ABC, the altitude from vertex C divides the hypotenuse...

Geometry - semicircle inside isosceles triangle - Isosceles triangle ABC has ...

geometry - how do you find the height of an isosceles triangle only knowing the ...

geometry - The medial triangle of a triangle ABC is the triangle whose vertices...

Geometry - Triangle ABC has vertices of A(0,0), B(–4,0)and C(–2,4). The ...

9th grade - given that a(-1,8) ,b(2,4) and if the line y=4 is the axis of ...

Geometry - The altitude to the hypotenuse of a right triangle ABC divides the ...