A line that is parallel to the graph of y=1/2+6 with a y-intercept of(0,-2)

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

Solve for q. -5(3-q) +4=5q-11

soldier1979 [14.2K]

Perform the indicated multiplication first: -15 + 5q + 4 = 5q - 11

Note that 5q appears on both sides of this equation. Cancelling, we get :

-11 = -11. This is always true. Thus, -5(3-q) +4=5q-11 is true for all q.

4 0

3 years ago

What is the measure of _C?

Pani-rosa [81]

Answer:

70°

Step-by-step explanation:

A+B+C=180°

70°+40°+C=180°

C=180°-110°

C=70°

4 0

3 years ago

Read 2 more answers

What is the answer to 3/2x - 5 = y

77julia77 [94]

Answer:

$x = \frac{2y + 10}{3}$

$y = \frac{3}{2}x -5$

Step-by-step explanation:

Hope this helps!

6 0

3 years ago

You are in $33 in eight hours at that rate how much would you earn in five hours

svp [43]

Answer:

20.625 dollars or about 20.63 dollars

Step-by-step explanation:

33/8 = 4.125

4.125 times 5 = 20.625

4 0

4 years ago