MATHEMATICS MIDDLE SCHOOL

Determine and prove what shape is formed for the given coordinates for ABCD, and then find theperimeter and area as an exact value.
A (10,-4), B (6,-7), C (3,-3), D (7,0)

Answers

Answer 1

Answer:

Answer:

Square

Step-by-step explanation:

Plot points A (10,-4), B (6,-7), C (3,-3), D (7,0) on the coordinate plane.

Find slopes of the sides:

$AB:\ (-7-(-4))/(6-10)=(3)/(4)\n \nBC:\ (-3-(-7))/(3-6)=-(4)/(3)\n \nCD:\ (0-(-3))/(7-3)=(3)/(4)\n \nDA:\ (-4-0)/(10-7)=-(4)/(3)$

The slopes of opposite sides are the same, so opposite sides are parallel. The slopes of adjacent sides have product of -1, then adjacent sides are perpendicular.

Find the lengths of all sides:

$AB=√((10-6)^2+(-4-(-7))^2)=√(4^2+3^2)=√(16+9)=√(25)=5\ units\n \nBC=√((6-3)^2+(-7-(-3))^2)=√(3^2+4^2)=√(16+9)=√(25)=5\ units\n \nCD=√((3-7)^2+(-3-0)^2)=√(4^2+3^2)=√(16+9)=√(25)=5\ units\n \nAD=√((10-7)^2+(-4-0)^2)=√(3^2+4^2)=√(16+9)=√(25)=5\ units\n \n$

All four sides are of the same length.

Quadrilateral ABCD is a square (all sides of equal length and perpendicular)

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Answers

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A.
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B.

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Answers

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Answers

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Answers

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Answers

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