Which of the following points lies on the circle whose center is at the origin and whose radius is 13?

Mathematics

1 answer:

Alexxandr [17]3 years ago

8 0

any point that is on the circle will have a distance of "radius" units, namely 13 units, since the radius is just that.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-5-0)^2+(12-0)^2}\implies d=\sqrt{(-5)^2+12^2} \\\\\\ d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13$

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The diagonals of this rhombus are 8 and 16 units long. Their intersection creates four right angles, two 4-unit-long segments, a

Roman55 [17]

Answer:

$64\ \text{sq. units}$

Step-by-step explanation:

Area of a rhombus is the product of the length of the diagonals divided by two.

Length of one diagonal is 8 units and the other diagonal is 16 units

Area is given by

$A=\dfrac{8\times 16}{2}\\\Rightarrow A=64\ \text{sq. units}$

The area of the rhombus is $64\ \text{sq. units}$

Another approach is the diagonals have created 4 triangles where the base and is height is either 4 units long or 8 units long so the area of the rhombus would be the area of the 4 triangles.

$A=4\times \dfrac{1}{2}\times 4\times 8\\\Rightarrow A=64\ \text{sq. units}$