Just numbers 9,10, and 11

Ivan used coordinate geometry to prove that quadrilateral EFGH is a square.

Gelneren [198K]

Answer:

(A)Segment EF, segment FG, segment GH, and segment EH are congruent

Step-by-step explanation:

Step 1

Quadrilateral EFGH with points E(-2,3), F(1,6), G(4,3), H(1,0)

Step 2

Using the distance formula

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Given E(-2,3), F(1,6)

$|EF|=\sqrt{(6-3)^2+(1-(-2))^2}=\sqrt{3^2+3^2}=\sqrt{18}=3\sqrt{2}$

Given F(1,6), G(4,3)

$|FG|=\sqrt{(3-6)^2+(4-1)^2}=\sqrt{3^2+3^2}=\sqrt{18}=3\sqrt{2}$

Given G(4,3), H(1,0)

$|GH|=\sqrt{(0-3)^2+(1-4)^2}=\sqrt{(-3)^2+(-3)^2}=\sqrt{18}=3\sqrt{2}$

Given E (−2, 3), H (1, 0)

$|EH|=\sqrt{(0-3)^2+(1-(-2))^2}=\sqrt{(-3)^2+(3)^2}=\sqrt{18}=3\sqrt{2}$

Step 3

Segment EF ,E (−2, 3), F (1, 6)

Slope of |EF|= $\frac{6-3}{1+2} =\frac{3}{3}=1$

Segment GH, G (4, 3), H (1, 0)

Slope of |GH| $= \frac{0-3}{1-4} =\frac{-3}{-3}=1$

Step 4

Segment EH, E(−2, 3), H (1, 0)

Slope of |EH| $= \frac{0-3}{1+2} =\frac{-3}{3}=-1$

Segment FG, F (1, 6,) G (4, 3)

Slope of |EH| $=\frac{3-6}{4-1} =\frac{-3}{3}=-1$

Step 5

Segment EF and segment GH are perpendicular to segment FG.

The slope of segment EF and segment GH is 1. The slope of segment FG is −1.

Step 6

Segment EF, segment FG, segment GH, and segment EH are congruent.

The slope of segment FG and segment EH is −1. The slope of segment GH is 1.

Step 7

All sides are congruent, opposite sides are parallel, and adjacent sides are perpendicular. Quadrilateral EFGH is a square

4 0

3 years ago

Read 2 more answers

Can someone help me to find length CD

uysha [10]

Answer:

CD = 3.602019190339

Step-by-step explanation:

CD = DA - CA

DA = DB×Cos(29) = 18.7×cos(29) = 16.355388523507

BA = BA×cos(43) = 18.7×cos(43) = 13.676314220278

CA = BA÷tan(47) = 13.676314220278÷tan(47) = 12.753369333168

Then

CD = 16.355388523507 - 12.753369333168 = 3.602019190339

7 0

4 years ago

Please help giving brainliest:)

Galina-37 [17]

Answer:

10*(9-5)

Step-by-step explanation:

8 0

3 years ago

1. Determine if the set of ordered pairs is a relation or a function.

kykrilka [37]

Answer:

This is just a relation.

Step-by-step explanation:

It is easy to see if a set of ordered pairs is a relation or a relation that is a function.

If all the points are distinct, then you just have to look at the $x$ -coordinates.

If all the $x$ -coordinates are different, then it is a function. Otherwise, it is a just a relation.

So this cannot be a function because there is at least two different points that have $x=0$ .

5 0

3 years ago

(2-3a)(8+5a) please help me

IceJOKER [234]

Answer:

-15a² -14a+16

Step-by-step explanation:

2×8=16

2×5a=10a

-3a×8=-24a

-3a×5a=-15a²

16+10a-24a-15a² = -15a² -14a+16

7 0

3 years ago