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3 years ago

If the trapezoid on the grid below is translated by using the rule (x,y)-> (x-4,y-3) what will be the coordinates of B’?

Mathematics

1 answer:

vesna_86 [32]3 years ago

6 0

Answer:

B'(3, 5)

Step-by-step explanation:

Rule for the translation of a point (x, y) by 'h' units left and 'k' units upwards,

(x, y) → (x - h, y + k)

If h = 4 and k = 3,

$(x, y)\rightarrow(x-4,y+3)$

Following this rule coordinates of the image point of B will be,

B(7, 2) → B'(7 - 4, 2 + 3)

→ B'(3, 5)

Therefore, coordinates of the image point B' will be,

B'(3, 5)

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3 years ago

A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangl

AysviL [449]

Answer:

The quadrilateral is not a rectangle

Step-by-step explanation:

we know that

If a quadrilateral ABCD is a rectangle

then

Opposite sides are congruent and parallel and adjacent sides are perpendicular

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

A(-5,5), B(1,8), C(4,2), and D(-2,-2)

Plot the figure to better understand the problem

see the attached figure

Find the slope of the four sides and then compare

step 1

Find slope AB

A(-5,5), B(1,8)

substitute in the formula

$m=\frac{8-5}{1+5}$

$m=\frac{3}{6}$

$m_A_B=\frac{1}{2}$

step 2

Find slope BC

B(1,8), C(4,2)

substitute in the formula

$m=\frac{2-8}{4-1}$

$m=\frac{-6}{3}$

$m_B_C=-2$

step 3

Find slope CD

C(4,2), and D(-2,-2)

substitute in the formula

$m=\frac{-2-2}{-2-4}$

$m=\frac{-4}{-6}$

$m_C_D=\frac{2}{3}$

step 4

Find slope AD

A(-5,5), D(-2,-2)

substitute in the formula

$m=\frac{-2-5}{-2+5}$

$m=\frac{-7}{3}$

$m_A_D=-\frac{7}{3}$

step 5

Verify if the opposites are parallel

Remember that

If two lines are parallel, then their slopes are the same

The opposite sides are

AB and CD

BC and AD

we have

$m_A_B=\frac{1}{2}$

$m_C_D=\frac{2}{3}$

$m_A_B \neq m_C_D$

It is not necessary to continue verifying, because two of the opposite sides are not parallel

therefore

The quadrilateral is not a rectangle

4 0

3 years ago

In the game of roulette, a player can place a $8 bet on the number 17 and have a StartFraction 1 Over 38 EndFraction probabili

svp [43]

Answer:

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Expected loss in 1000 games: $421

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The expected value for a single game is:

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The expected value of the game is -$0.421

In 1,000 plays, the expected loss is:

$L = 1,000*-\$0.421\\L=-\$421$

You would expect to lose $421.

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Answer:

Step-by-step explanation:

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4 years ago

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