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3 years ago

Prove that the figure is a parallelogram. If so, classify the parallelogram. Be specific and justify your answer.

Mathematics

1 answer:

sesenic [268]3 years ago

8 0

Answer:

Step-by-step explanation:

If it is a parallelogram the opposite sides will a have the same slope.

Using the diagram we see from the coordinates of A and B:

Slope of AB = (5 - -1)/(-1 - -5)

= 6/4

= 3/2.

In the same way

slope of CD = (2 - -4) / (1 - -3)

= 3/2.

So AB and CD can be shown to be parallel.

Similarly the lines BC and AD are parallel.

So the figure is a parallelogram

Finding the perimeter (counting the units between the points):

Perimeter = 2AB + 2BC

By Pythagoras:

AB = sqrt (6^2 + 4^2) = sqrt 52

BC = sqrt (3^2 + 2^2) = sqrt 13

So Perimeter = 2sqrt52 + 2sqrt13

= 4sqrt13 + 2 sqrt13

= 6sqrt13

or 21.63 unit^2 to 2 decimal places.

Area = sqrt52 * perpendicular distance between the lines AB and CD.

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3 years ago

Find the midpoint of the line segment defined by the points: (5, 4) and (−2, 1) (2.5, 1.5) (3.5, 2.5) (1.5, 2.5) (3.5, 1.5)

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Answer:

$\boxed {\boxed {\sf (1.5 , 2.5)}}$

Step-by-step explanation:

The midpoint is the point that bisects a line segment or divides it into 2 equal halves. The formula is essentially finding the average of the 2 points.

$(\frac {x_1+x_2}{2}, \frac {y_1+ y_2}{2})$

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 endpoints of the line segment. For this problem, these are (5,4 ) and (-2, 1).

x₁= 5
y₁= 4
x₂= -2
y₂= 1

Substitute these values into the formula.

$( \frac {5+ -2}{2}, \frac {4+1}{2})$

Solve the numerators.

5+ -2 = 5-2 = 3
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$( \frac {3}{2}, \frac{5}{2})$

Convert the fractions to decimals.

$(1.5, 2.5)$

The midpoint of the line segment is (1.5 , 2.5)

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