Please help me with full calculation

9514 1404 393

  a. 12

  b. 15

  c. (2, -2.5)

Step-by-step explanation:

a. The points lie on a horizontal line, so the distance between them is the difference of their x-coordinates: 4 -(-8) = 12 units.

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b. The length BD is the diagonal of the rectangle. Its length is given by the distance formula as ...

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((-8 -4)^2 +(-7 -2)^2) = √((-12)^2 +(-9)^2) = √(144 +81) = √225

  d = 15

The distance between B and D is 15 units.

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c. The midpoints of AC and BD are the same:

  (A +C)/2 = ((-8, 2) +(4, -7))/2 = (4, -5)/2 = (2, -2.5)

  (B +D)/2 = ((4, 2) +(-8, -7))/2 = (4, -5)/2 = (2, -2.5)

Point (2, -2.5) can be used to locate the lake.