given the vertics of a triangle, for example a(3,2), B (-5,-1).C(-2,-8), how would you determine whe

plot the points and look at the triangle

calculate the slopes (gradients) of each line

lines at right angles have slopes that are negative reciprocals of each other(except 0)

Using the given coordinates, calculate the lengths of the three sides. If it is a right triangle, the Pythagorean Principle will apply and the square of the longest side (hypotenuse) will equal the sum of the squares of the two smaller sides.

nice one george

although it's an exercise in determining the gradient

OK then relocate the origin of coordinates to Point B, & get new coordinates for Points A & C simply by by subtracting the corresponding old coordinates of Point B from those of A & C. Then take the inner product of the vectors to Points A and C using their new coordiantes. If it is zero the vectors are orthogonal and the triangle is a right triangle.

love-kiran143
i'm 50 years old and have no idea so dont worry if you dont either. just focus on each individual step. my eyes glazed over as i try to read georges post.

on what will i plot the points?
what does a(3,2) mean?
what are vertics?

S/he should have SOME idea if s/he's in a geometry class though.

Vertices are corners. These three points are the corners of a triangle. You plot them on an x/y axis. You can draw it yourself on graph paper by making two perpendicular lines that divide the paper into four quadrants of the same size. You put a 0 where the lines meet. To the left of the horizontal axis (x) the numbers are negative. To the right they're positive. Above the 0 on the vertical axis (y) the numbers are positive, below they are negative. So if you have the point (3,2) you count three squares to the right of the 0 and two squares up from there and make a dot. The first number ALAYS refers to the x axis and the second number ALWAYS refers to the y. Then you do the same thing for your other points.

I- like George- read the problem to be asking if the resulting triangle you draw - once you plot all three points and connect the dots with lines you draw- is a right triangle. This means, does it have a right angle? I don't read the problem to be asking slope - although you can also do it that way. So if the product of the length of the hypoteneuse (the longest side- which would be across from the right angle) is equal to the product of each of the two shorter sides squared and then added together - you have your answer. That's the way I'd do it - I think that's the most direct and easiest - and I think your teacher wants you to work mainly on plotting points here - unless s/he also gave you the formula for slope.

I left out the word 'squared' when talking about the hypoteneuse. You have to square that too.

Thanks for the simplified explanaton aiden i suspect kiran knows more about this than i do bit there was a reason i asked.

The sum of the square of the two sides equals the square of the hypotonuse.
a2+b2=c2
(where 2 = squared cause i cant do superscript)

if i wanted to work out "slope" i'd use a clinometer.

Both approaches work and neither is especially difficult, but I think the slope one is by far the easiest. Calculating three slopes is very straightforward and you just leave them as ratios. No squaring, no simplifying radicals.

Given: A(3,2), B (-5,-1).C(-2,-8) then
AB = -3/-8
BC = -7/3
AC = -10/-5

No right triangle. It's also clear from this approach how to make it a right triangle. If BC was -8/3, you would have a right triangle, so move C to (-3,8).

Additonally if you were to plot it and draw lines between the dots, you could measure the angles with a protractor. If one of the angles = 90 degrees, it's a right triangle.

You could do that but in the problem presented angle B is 92.6 degrees, so you better draw it very cleanly and measure it accurately.

Good point. You are so smart bro!