Write a coordinate proof to prove that in an isosceles right triangle, the segment from the vertex of the right angle to the midpoint of the hypotenuse is perpendicular to the hypotenuse

In an isosceles right triangle, the segment from the vertex of the right angle to the midpoint of the hypotenuse is perpendicular to the hypotenuse is proved

Solution:

Let we have a isosceles right angle triangle with coordinate O(0,0),A(k,0),B(0,k).  

Here OA = OB and AB is the hypotenuse of the isosceles right angle triangle and according to question, the coordinates of midpoint M of hypotenuse is (k/2,k/2).

Now we know that the Slope of vertex is  

  --- eqn 1

Now for Slope of line AB,

--- eqn 2

on multiplying eq 1 and 2 we get

Since slope of AB multiplied with slope of OM is equal to -1. That means line AB is perpendicular to line OM

Hence in an isosceles right triangle, the segment from the vertex of the right angle to the midpoint of the hypotenuse is perpendicular to the hypotenuse is proved

yes, gavin is right.

step-by-step explanation:

gavin is correct. 

this problem is about converting 9% per year to how many percent per quarter. the rate is still the same. it only differed in the time period. so, through dimensional analysis,

9% per year  × (1 year / 4 quarters) = 2.25% per quarter

if he was asked to convert 9% per year to how many percent per quarter  compounded quarterly, then you will not simply divide by four. this is because compounding is not linear.

hope this , have a good day. c;