Mathematics, 23.10.2020 17:40 27lcasselberry

Which of the following would be a line of reflection that would map ABCD onto itself? A. y = 2
B. 3x + y = 1
C. 3x + y = −1
D. −3x + 3y = 9

Which of the following would be a line of reflection that would map ABCD onto itself?

A. y = 2
B.

Answers: 2

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Answers

Answer from: AnNguyen

D) -3x + 3y = 9.

Step-by-step explanation:

Any line that cuts the figure in two equal halves will be a solution of this problem.

For example, the lines y = 1 and x = -2 cut the square in two equal halfves.

Now, the other two lines that cut the square in two equal halfves are the lines:

AC and BD.

Let's find the equations for these lines:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

The line AC is:

A = (-3, 0) C = (-1, 2)

The slope of this line is:

a = (2 - 0)/(-1 - (-3)) = 1

y = 1*x + b

And when x = -1, we have that y = 2.

Then:

2 = 1*-1 + b

2 + 1 = b

Then the line AB is:

y = 1*x + 3.

Now, if we multiply both parts of the equation by the same number, the line does not change.

Multiply both sides by 3:

3*y = 3*x + 9.

Let's put our two variables on the left side and get:

-3x + 3y = 9

This is option D, then D is a correct option.

Now let's analyze the line BD.

B = (-3, 2) and D = (-1, 0)

The slope is:

a = (0 - 2)/(-1 - (-3) = -1

y = -1*x + b

And we know that when x = -1, y = 0 then:

0 = -1*-1 + b

1 = b

Then this line is:

y = -1*x + 1.

This line does not fit with any of the given options.

Then the only correct option is:

D) -3x + 3y = 9.

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

8- 2 = 6sally have 6 cars now.

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Which of the following would be a line of reflection that would map ABCD onto itself? A. y = 2