Question

Geometry! please help!

Answer 1

9514 1404 393

Answer:

1. rhombus
2. square
3. rectangle
4. square

Step-by-step explanation:

It is convenient to look at the differences of end point coordinates.

For a square, the values will be interchanged and one negated.

For a rhombus, the dot product will be zero.

For a rectangle, their sum of squares (diagonal length) will be the same.

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1. VX = X - V = (11 -3, 4 -0) = (8, 4)

  WY = Y -W = (8 -6, 0 -4) = (2,-4)

The numbers are different, so it is not a square. The dot product is ...

 (8)(2) + (4)(-4) = 16 -16 = 0

So, the figure is a rhombus.

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2. LN = (6 -1, 3 -2) = (5, 1); MP = (4 -3, 0 -5) = (1, -5)

The figure is a square.

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3. HK = (12 -1, 0 -3) = (11, -3); JL = (3 -10, -3 -6) = (-7, -9)

The lengths of the diagonals are ...

  √(11^2 +3^2) = √130  and  √(7^2 +9^2) = √130

Diagonals are the same length, so the figure is a rectangle.

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4. EG = (-2 -(-4), -1 -3) = (2, -4); FH = (-5 -(-1), 0 -2) = (-4, -2)

The figure is a square.