Question

HELP! If A = (1, 1) B = (3, 3) and C = (5, 1), classify the the following triangle as either equilateral or isosceles. Type the word equilateral or isosceles in the blank.

Answer for Blank 1:

Answer 1

http://www.wolframalpha.com/input/?i=triangle+%28+%281%2C+1%29+%2C+%283%2C+3%29+%2C+%285%2C+1%29%29

Answer 2

isosceles right triangle

Answer 3

Answer is isosceles,
As from distance formula you have \[AB=\sqrt{(3-1)^2+(3-1)^2}=\sqrt{8}\]

similarly you can have BC and AC (from which you'll get AC=sqrt(16) and BC = sqrt(8))

As, AB=AC but not equal to BC. Hence triangle is isosceles

Answer 4

Thanks to you both can you he lp with another one?

Answer 5

The following set of coordinates represents which figure?

(3, -5), (5, -2), (10, -4), (8, -7)

Parallelogram

Rectangle

Rhombus

Square

Answer 6

The next question is this

Quadrilateral ABCD has coordinates A (3, -5), B (5, -2), C (10, -4), D (8, -7). Quadrilateral ABCD is a

rectangle, because opposite sides are congruent and adjacent sides are perpendicular

square, because all four sides are congruent and adjacent sides are perpendicular

parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular

rhombus, because all four sides are congruent and adjacent sides are not perpendicular

Answer 7

Use the same distance equation that I'd used above (of course if you don't want to plot those points on a graph, either you can do that in that way also). The equation is,
\[d=\sqrt{(x_1-x_2)^2+(y_1-y_2)}\]
put the respective values and check the distance AB, BC, CD and DA. Wait it's not over...
Now what is all the sides are equal (which can result in square OR rhombous) or opposite two sides equal (which can result either in parallelogram or rectangle).
For this just compare the diagonals (i.e AC and BD). If they are equal the they will result in square for first case and rectangle for second case

Answer 8

So confused

Answer 9

I'll recommend you to go with graph first. http://www.wolframalpha.com/input/?i=quadrilateral%28+%283%2C+-5%29+%2C+%285%2C+-2%29+%2C+%2810%2C+-4%29+%2C+%288%2C-7%29%29

Answer 10

Oh wow I'm stupid now it makes sense

Answer 11

Try this video on Distance Formula: https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/v/distance-formula

And after that try some problems here: http://www.regentsprep.org/Regents/math/geometry/GCG3/PracDistance.htm

Doing self assessment will surely help. And never accept the direct answers. Always try to make your own approach.

Answer 12

Thanks