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ikadub [295]
3 years ago
6

Wha is the area of a rectangle with vertices at (4, 3), (11, 3), (11,9), and (4, 9)?

Mathematics
2 answers:
Butoxors [25]3 years ago
8 0

Answer:

42 units^2.

Step-by-step explanation:

We are given that it is a rectangle so its area is the product of the length of adjacent sides.

Length  of the horizontal line = 11 - 4 = 7 units ( from the first 2 points) and  the length of an adjacent side is 9 - 3 = 6 units (from the second and third points).

Area = 7 * 6 = 42.

tia_tia [17]3 years ago
4 0

Answer:

area of rectangle = 42

Step-by-step explanation:

area of rectangle = length × width

                             = 7 × 6

                             = 42

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Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)
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Answer:   \bold{y=-\dfrac{1}{3}x-1}

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

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First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\

Next, find the midpoint of (4, 1) and (2, -5):

Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\


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