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Black_prince [1.1K]
3 years ago
7

Use complete sentences to describe how measurements of position in two directions (vertical and horizontal) are sufficient enoug

h to describe the position of an object on a flat surface
Mathematics
1 answer:
posledela3 years ago
5 0

Answer:

We know that our world is in 3 dimensions i.e. there are three directions and so, three co-ordinates are required.

Now, if we have to find a position of an object lying on a flat surface, this means that there are only two directions and so, two co-ordinates are needed.

So, we can define the domain ( xy-axis ) in such a way that there are two axis - horizontal where right area have positive values & left area has negative values and vertical where upward side have positive values & downward side has negative values.

For e.g. if we want to find the position of a pen on the table. We will make our own xy-axis and see in which quadrant the pen lies.

Let us say that the pen lies at (2,3), this means that the position of pen is in the first quadrant or it is 2 units to the right of y-axis and 3 units up to the x-axis.

This way we can see that two directions are sufficient to find the position of an object placed on a flat surface.

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Answer:

Therefore the Area of Rhombus ABCD is 36 unit².

Step-by-step explanation:

Given:

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We know that Area of Rhombus is given as

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Where ,

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We have,

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Using Distance Formula we get

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Substituting coordinates A and C we get

l(AC) = \sqrt{((-1-(-1))^{2}+(-6-0)^{2} )}=\sqrt{36}\\l(AC)=6\ unit

Similarly for BD we have,

l(BD) = \sqrt{((5-(-7))^{2}+(-3-(-3))^{2} )}=\sqrt{144}\\l(BD)=12\ unit

Now Substituting AC and BD in Formula we get

\textrm{Area of Rhombus}=\dfrac{1}{2}\times AC\times BD

\textrm{Area of Rhombus}=\dfrac{1}{2}\times 6\times 12=36\ unit^{2}

Therefore the Area of Rhombus ABCD is 36 unit².

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