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3 years ago

What is the ordered pair of C′ after point C (1, 2) is rotated 90° clockwise?

Mathematics

2 answers:

Ahat [919]3 years ago

7 0

Answer: (2,-1)

Step-by-step explanation:

The rule for rotation of a shape about 90° clockwise is given by :-

$(x,y)\rightarrow(y,-x)$ [i.e. interchange x by y and y by negative of x ]

Given point : C (1, 2)

When point C is rotated 90° clockwise , then the ordered pair for its image C' will be :-

$C(1,2)\rightarrow (2,-1)$

Hence, the ordered pair of C′ after point C (1, 2) is rotated 90° clockwise = (2,-1).

ivolga24 [154]3 years ago

4 0

Answer:

C'(2,-1)

Step-by-step explanation:

1) Transform point C(1,2) to polar coordinates.

C(1,2)=C(x,y)=C(r,tetha)=C(squareroot(5),63.44Degrees)

2) Substract 90 degress to get C'

C'=(squareroot(5),-26.56)

3) Transform point C' to cartesian coordinates.

C'=(x,y)=(squarerott(5)cos(-26.56),squareroot(5)sin(-26.56)

=C'(2,-1)

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Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

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a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. $\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\$

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b) To find area of one lateral surface:

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Using equation (1) to find the area:

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c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

$\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}$

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Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

$\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^{2}$

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b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

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