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.

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length

now

AB:=units

BC:=units

AC:=units

C. the figure:

By using Pythagoras law

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

hypotenuse [h]=BC

we have

h²=p²+b²

substituting value

()²=2p²

16*5=2*()²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.

Step-by-step explanation:

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length \sqrt{(x2-x1)²+(y2-y1)²}

(x2−x1)²+(y2−y1)²

now

AB:\sqrt{(-2-0)²+(3+3)²}

(−2−0)²+(3+3)²

=2\sqrt{10}2

10

units

BC:\sqrt{(0-4)²+(-3-5)²}

(0−4)²+(−3−5)²

=4\sqrt{5}4

5

units

AC:\sqrt{(-2-4)²+(3-5)²}

(−2−4)²+(3−5)²

=2\sqrt{10}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\sqrt{5}4

5

)²=2p²

16*5=2*(2\sqrt{10}2

10

)²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.