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3 years ago

9

The segment that connects points (-2,8) and (3,-4) forms the diagonal of a rectangle. What are the lengths of the sides and diag

onal of the rectangle?

1 answer:

Rasek [7]3 years ago

4 0

Answer:the lengths of the sides of the rectangle are 5 units and 12 units the length of the diagonal of the rectangle is 13 units

Step-by-step explanation:

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Answer:

$\huge{ \boxed{ \bold{ \sf{y = - 2x + 6}}}}$

☥ $\tt{Question} :$

Write the equation of a line in slope - intercept form that has a slope of -2 and passes through the point ( - 1 , 8 ).

☥ $\tt{Step - \: by \: - \: step \: explanation}$

☪ $\underline{ \underline{ \text{Given : }}}$

Slope ( m ) = -2
Given point = ( - 1 , 8 )

☪ $\underline {\underline{ \text{To \: find}}} :$

Equation of a line in slope - intercept form ( i.e y = mx + c )

Let the point ( -1 , 8 ) be ( x₁ , y₁ )

☪ $\underline{ \underline{ \text{Solution}}} :$

$\underline{ \sf{y - y1 = m(x - x1)}}$

plug the known values :

↦ $\text{y - 8 = - 2 \{ x - ( - 1) \} }$

↦ $\text{y - 8 = - 2(x + 1)}$

Distribute -2 through the parentheses :

↦ $\text{y - 8 = - 2x - 2}$

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↦ $\boxed{ \text{y = - 2x + 6}}$

And we're done !

Hope I helped!

♡ Have a wonderful day / night ツ

~TheAnimeGirl ♪

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Someone explain this to me

e-lub [12.9K]

Answer: a) y = f(x - 6)

b) y = f(x) - 2

<u>Step-by-step explanation:</u>

For transformations we use the following formula: y = a f(x - h) + k

a = vertical stretch
h = horizontal shift (positive = right, negative = left)
k = vertical stretch (positive = up, negative = down)

a) f(x) has a vertex at (-1, 1)

M has a vertex at (5, 1)

The vertex shifted 6 units to the right → h = +6

Input h = +6 into the equation and disregard "a" and "k" since those didn't change. ⇒ y = f(x - 6)

b) f(x) has a vertex at (-1, 1)

N has a vertex at (-1, -1)

The vertex shifted down 2 units → k = -2

Input k = -2 into the equation and disregard "a" and "h" since those didn't change. ⇒ y = f(x) - 2

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3 years ago