SOLUTION: A triangle ABC has vertices A(1,3) ; B(1,-2) and C(-4,-2) : Which of the following is/are true? A. d(B;C) = {{{sqrt(41)}}} B. ∠C = 90° C. The midpoint of the hypotenuse

First you draw the triangle on graph paper:



Then we check out each answer:

We can just count the blocks from B to C since BC is
horizontal and find that the distance from B to C is 5,
so if it's 5, it's NOT 

We can certainly see from the graph that ∠C in NOT 90°,
since it is an acute angle much smaller than 90°.  It's
∠B that's 90°, not ∠C.

That's the only one left, so it must be the one that's true, 
since the others are false.  But let's see why anyway.

We use the midpoint formula:

Midpoint = 

The hypotenuse is AC, so we substitute:

x1 = x-coordinate of A = 1
x2 = x-coordinate of C = -4
y1 = y-coordinate of A = 3
y2 = y-coordinate of C = -2

Midpoint of AC = 
Midpoint of AC = 
Midpoint of AC = 

So we see this is the only one that is true.

Edwin