CAB is similar to EFD. What is the length of DE?

Given quadrilateral EFGH at e(-4,7) f(8,4) G(t,-5) and h(-7,-1) using coordinate geometry prove EFGH is a rectangle

Tcecarenko [31]

The above question was not properly written.

Complete Question

Given quadrilateral EFGH with vertices at E(-4,8), F(8,4), G(5,-5) and H(-7,-1), prove using coordinate geometry that EFGH is a rectangle.

Answer:

Quadrilateral EFGH is a rectangle.l because:

EF = GH and FG = EH

Step-by-step explanation:

The formula for coordinate geometry is given as :

√(x2 - x1)² + (y2 - y1)² when we have coordinates: (x1, y1) and (x2 , y2)

For the quadrilateral EFGH with given coordinates above to be a rectangle,

EF = GH

FG = EH

Hence:

For side EF

E(-4,8), F(8,4)

= √(8 - (-4))² + (4 - 8)²

= √12² + -4²

= √144 + 16

= √160 units

For side FG

F(8,4), G(5,-5)

=√(5 - 8)² + (-5 - 4)²

= √-3² + -9²

= √9 + 81

= √90 units

For Side GH

G(5,-5) , H(-7,-1)

= √(-7 - 5)² + (-1 - (-5))²

= √-12² + 4²

= √144 + 16

= √160 units

For side EH

E(-4,8), H(-7,-1)

= √(-7 -(-4))² +(-1 - 8)²

= √-3² + -9²

= √9 + 81

= √90 units

From the above calculation, we can see that truly,

EF = GH

FG = EH

Therefore, quadrilateral EFGH is a rectangle.

6 0

3 years ago

Which expression represents "the sum of 5 and b divided by two

DIA [1.3K]

Step-by-step explanation:

<u>Break down the word expression:</u>

The sum of 5 and b divided by two

the sum (+) of 5 and b (5 + b) divided by 2.

<u>Expression:</u>

$\frac{(b + 5)}{2}$

Parentheses represent that we need to add first, in order to divide the sum by 2.

5 0

3 years ago

Please show me How to do this number

VARVARA [1.3K]

Ok, so you have the range correct. It is 120<___<150 (It should be less than or equal to, but there's no symbol for that, to my knowledge.) But the term in the middle shouldn't be .25x The reason is because that actually quadruples the price in the end, as you seem to have found out. Rather, instead of multiplying x by .25, multiply the numbers in the range by .75. Here's why: When you reduce something in price by 25%, you are paying for 75% of the original price. Not 25%. That would be a 75% discount. So, in all actuality,your answer would be $90

6 0

3 years ago

You and your friend drive toward each other. The equation 50h = 190 – 45h represents the number h of hours until you and your fr

Evgesh-ka [11]

Answer:

C. 2 hours

Step-by-step explanation:

50h= 190-45h

50h + 45h = 190

95h = 190.

190÷95= 2h

8 0

3 years ago

a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and

fomenos

Answer:

The time taken for the upward motion is 1 second. The same time is taken for the downward motion

It reaches a maximum height of 4.9 meters.

Step-by-step explanation:

The equation of motion is:

$x(t) = -4.9t^{2} + 9.8t$

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format $x(t) = at^{2} + bt + c$