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Luba_88 [7]
3 years ago
14

Some one help me i cant get it

Mathematics
1 answer:
Novay_Z [31]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

(a)

Under a rotation of 180° about the origin

a point (x, y ) → (- x, - y)

the coordinates of P, Q and R are

P(1, -1 ), Q(3, - 2 ), R(3, - 4 )

Hence under the given rotation

P(1, - 1 ) → P'(- 1, 1 )

Q(3, - 2 ) → Q'(- 3, 2 )

R(3, - 4 ) → R'(- 3, 4 )

(b)

Under a reflection in the x-axis

a point (x, y ) → (x, - y ), hence

P(1, - 1 ) → P''(1, 1 )

Q(3, - 2 ) → Q''(3, 2 )

R(3, - 4 ) → R''(3, 4 )


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3 0
2 years ago
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alisha [4.7K]

Answer:

d=3\sqrt{2}\ units

Step-by-step explanation:

<u><em>The complete question is</em></u>

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{9-5}{7-3}

m=\frac{4}{4}=1

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=1\\point\ (3,5)

substitute

y-5=(1)(x-3)

isolate the variable y

y=x-3+5

y=x+2 -----> equation A

step 2

Find the equation of the perpendicular line to the given line L  that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

so

The slope of the given line L  is m=1

The slope of the line perpendicular to the given line L  is

m=-1

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=-1\\point\ (2,10)

substitute

y-10=-(x-2)

isolate the variable y

y=-x+2+10

y=-x+12 ----> equation B

step 3

Find the intersection point equation A and equation B

y=x+2 -----> equation A

y=-x+12 ----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

(2,10) and (5,7)

substitute

d=\sqrt{(7-10)^{2}+(5-2)^{2}}

d=\sqrt{(-3)^{2}+(3)^{2}}

d=\sqrt{18}\ units

simplify

d=3\sqrt{2}\ units

see the attached figure to better understand the problem

6 0
3 years ago
75 out of 300 oranges in a basket are bad. what percent age of the oranges are (a) bad (b)good
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Answer:

a) 25% are bad

b) 75% are good

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We know that there are 300 oranges total and that 75 are bad. That means that the rest are good (implied).

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So to find the percentage we have to take the selected amount divided by the total amount.

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However, that's a decimal or <em>a number out of 1, </em>we need a percent or <em>a number out of 100.</em> So we have to multiply both numbers by 100.

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It says Sandeep has twice as much as Sonia. Thus, let Sandeep's amount be 2x and Sonia's amount be x.

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