Question

A. What are the coordinates of the vertices of the triangle below?

B. Find each side length.
C. Classify the figure. Use coordinate geometry (i.e. Pythagorean Theorem, distance formula,
slope formula, etc.) and properties of triangles to justify your response.

Answer 1

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length
`√((x2-x1)²+(y2-y1)²)`

now

AB:
`√((-2-0)²+(3+3)²)`=
`2√(10)`units

BC:
`√((0-4)²+(-3-5)²)`=
`4√(5)`units

AC:
`√((-2-4)²+(3-5)²)`=
`2√(10)`units

C. the figure:

By using Pythagoras law

base[b]=AB=perpendicular [p]=AC

hypotenuse [h]=BC

we have

h²=p²+b²

substituting value

(
`4√(5)`)²=2p²

16*5=2*(
`2√(10)`)²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.