Answered

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Nikki drew a rectangle with a perimeter of 18 units on a coordinate grid. Two of the vertices were (4, –3) and (–1, –3). What could be the coordinates of the other two vertices of the rectangle?

Sagot :

xero099

Answer:

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)

Step-by-step explanation:

Geometrically speaking, the perimeter of a rectangle ([tex]p[/tex]) is:

[tex]p = 2\cdot b + 2\cdot h[/tex] (1)

Where:

[tex]b[/tex] - Base of the rectangle.

[tex]h[/tex] - Height of the rectangle.

Let suppose that the base of the rectangle is the line segment between (4, -3) and (-1, -3). The length of the base is calculated by Pythagorean Theorem:

[tex]b = \sqrt{[(-1)-4]^{2}+[(-3)-(-3)]^{2}}[/tex]

[tex]b = 5[/tex]

If we know that [tex]p = 18[/tex] and [tex]b = 5[/tex], then the height of the rectangle is:

[tex]2\cdot h = p-2\cdot b[/tex]

[tex]h = \frac{p-2\cdot b}{2}[/tex]

[tex]h = \frac{p}{2}-b[/tex]

[tex]h = 4[/tex]

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)

View image xero099
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