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3 years ago

Triangle ABC is transformed with the center of dilation at the origin.

1 answer:

6 0

Dilation is a transformation that maps an object to an image by stretching or diminishing it but retaining the original shape. It is described by stating the center of dilation and the dilation scale factor.
Dilation scale factor is given by dividing the coordinate of the image with the corresponding coordinate of the object.
In this case, if we consider A and A' then; k(-5,-4) = (-3.75, -3)
Thus, -5k = -3.75 or -4k = -3
k = 3/4
Hence the scale factor of dilation is 3/4

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The center of the inscribed circle of Triangle ABC is point , and the center of the circumscribed circle of Triagnle ABC is poin

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Answer:

Part A: The center of The inscribed circle is the point S

Part B: The center of The circumscribed circle is the point P

Step-by-step explanation:

Part A: Find the center of The inscribed circle of ΔABC

The inscribed circle will touch each of the three sides of the triangle in exactly one point,

The center of the inscribed circle is the point of intersection between the angle bisectors of the triangle.

So, According to the previous definition:

A₁A₂ and B₁B₂ are the angle bisectors of ∠A and ∠B

So, the inter section between them is the center of The inscribed circle

So, the center of The inscribed circle is the point S

=====================================================

Part B: Find the center of The circumscribed circle of ΔABC

The circumscribed circle is the circle that passes through all three vertices of the triangle.

The center of the circumscribed circle is the point of intersection between the perpendicular bisectors of the sides.

So, According to the previous definition:

P₁P₂ and Q₁Q₂ are the perpendicular bisectors of AB and BC

So, the inter section between them is the center of The circumscribed circle

So, the center of The circumscribed circle is the point P

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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(b) 2sin(theta) + 1/sin(theta) - 1 = 0 for 0 <_ x < 2x

Lady bird [3.3K]

Answer:

2 - 2 cos²x = sin x

2 = sin x + 2 cos² x

0 = -2 + sin x + 2(1 - sin² x)

0 = -2 sin² x + sin x + 2 - 2

0 = 2 sin² x - sin x 0 = sin x (2 sin x - 1)

sin x = 0 v sin x = 0.5

x10° + k.360° x1 = 0°, 360°

x2 = (180° - 0°) + k.360°

x2 = 180°

x3 = 30° + k.360°

x3 = 30°

x4 = (180° -30°) + k.360° x4 = 150°

HP: {x | 0°, 30°, 150°, 180°, 360°)

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2 years ago

Triangle ABC ​is transformed with the center of dilation at the origin.

Triangle ABC is transformed with the center of dilation at the origin.