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leva [86]
4 years ago
12

Please Help!!!!!! So i know how to reflect over line y=-x but how would i do it over line y=-x+6. An example would be helpful an

d a rule for more problems of this kind.
Mathematics
1 answer:
Westkost [7]4 years ago
4 0
To reflect in the line y = -x + 6, we translate everything down 6 first. This will make it seem like we are reflecting in the line y = -x
                                 (x,y) → (x, y-6)
Then, to reflect in the line y = -x, we switch the x- and y-coordinates and then make them negative
                                 (x,y) → (-(y-6), -x)     
Then we move everything back up again
                                 (x,y) → (-(y-6), -x + 6)          
I will present to you an example. Reflect the point (-4, 8) in the line y = -x + 6.
                                 (-4,8) → (-(8-6), -(-4) + 6) → (-2, 10)
You should graph this out to confirm with the reflection line.
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65% out of what number is 39

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y=7x

Step-by-step explanation:

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Translate the phrase into an algebraic expression.
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8 + \frac{5}{w}

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A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What
GalinKa [24]

Answer:

(1) The slope of the line segment AB is 1.\bar 3

(2) The length of the line segment AB is 10

(3) The coordinates of the midpoint of AB is (5, 7)

(4) The slope of a line perpendicular to the line AB is-0.75

Step-by-step explanation:

The coordinates of the line segment AB are;

A(2, 3) and B(8, 11)

(1) The slope of a line segment is given by the following equation;

Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

Where;

(x₁, y₁) and (x₂, y₂) are two points on the line segment

Therefore;

The slope, m, of the line segment AB is given as follows;

A(2, 3) = (x₁, y₁) and B(8, 11) = (x₂, y₂)

Slope, \, m_{AB} =\dfrac{11-3}{8-2} = \dfrac{8}{6}  = 1 \frac{1}{3} = 1.\bar3

The slope of the line segment AB = 1.\bar 3

(2) The length, l, of the line segment AB is given by the following equation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Therefore, we have;

l_{AB} = \sqrt{\left (11-3  \right )^{2}+\left (8-2  \right )^{2}} = \sqrt{64 +36} = 10

The length of the line segment AB is 10

(3) The coordinates of the midpoint of AB is given as follows;

Midpoint, M = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )

Therefore;

Midpoint, M_{AB} = \left (\dfrac{2 + 8}{2} , \ \dfrac{3 + 11}{2} \right ) = (5, \ 7)

The coordinates of the midpoint of AB is (5, 7)

(4) The relationship between the slope, m₁, of a line AB perpendicular to another line DE with slope m₂, is given as follows;

m_1 = -\dfrac{1}{m_2}

Therefore, the slope, m₁, of the line perpendicular to the line AB, that has a slope m₂ = 4/3 = 1.\bar 3 is given as follows;

m_1 = -\left (\dfrac{1}{\frac{4}{3} } \right ) = -\dfrac{3}{4}  = -0.75

The slope, m₁, of the line perpendicular to the line AB is m₁ = -0.75.

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