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3 years ago

What will be the new position of the given point after rotating 180 about the origin

Mathematics

2 answers:

quester [9]3 years ago

5 0

Answer:

" Rotation of a point through 180°, about the origin when a point M (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, it takes the new position M' (-h, -k) " .

Hence, the rotations of the given point could be represented by the help of the figure attached to the answer.

Hence in the first part the given point is in first quadrant but after the rotation it will move to third quadrant.

similarly in second option the point is in third quadrant and hence it will transform to the first quadrant.

and in last position the point is in fourth quadrant and hence it will transform to second after rotation by 180 degree.

leva [86]3 years ago

4 0

Answer: a) First quadrant

Step-by-step explanation:

From the given picture, the position of the given point is in third quadrant.

Every point in third quadrant are in the form of (-a,-b), where a and b are any positive numbers [both x and y axis are negative there]

Also after rotation of 180° the point (x,y) will map to (-x,-y)

therefore, after rotation of 180° the point (-a,-b) will map to

(-(-a),-(-b))=(a,b), where a and b are any positive numbers

Thus, the coordinate of image point =(a,b)

Since both x and y coordinate of the image are positive therefore it must lie in the first quadrant.

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2 years ago

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x-y=

Bond [772]

Answer:

The system of linear equations has infinitely many solutions

Step-by-step explanation:

Let's modified the equations and find the answer.

Using the first equation:

$2x-y=5$ we can multiply by 2 in both sides, obtaining:

$2*(2x-y)=2*5$ which can by simplified as:

$4x-2y=10$ which is equal to:

$4x=2y+10$

Considering the second equation:

$=4x+ky=2$

Taking into account that from the first equation we know that: $4x=2y+10$ , we can express the second equation as:

$2y+10+ky=2$ , which can be simplified as:

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$(2+k)y=-8$

$y=-8/(2+k)$

Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:

$2+k=0$ if $k=-2$

This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.

For example, if k=0 then

$y=-8/(2+0)$ which give us y=-4, and, because: