Need so much help please

How can ΔABC be mapped to ΔXYZ?

avanturin [10]

Answer: (B) vertex B vertex Y

Step-by-step explanation:

Just Thought I Should Help Anyone Out For GEOMETRY ; ) BTW im a girl

6 0

3 years ago

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Pythagorean Theorem & irrational Numbers Question

Arisa [49]

Answer:

2nd

Step-by-step explanation:

6 0

3 years ago

20= -x + (x squared) solve for x

MArishka [77]

Answer:

Step-by-step explanation:

x = 5

x= -4

3 0

2 years ago

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Enter the slope-intercept equation for the image of line ℓ after a clockwise rotation of 90°. (Hint: To find the image of line ℓ

Free_Kalibri [48]

Answer:

y = -2x - 2

Step-by-step explanation:

From the graph attached,

If the line 'l' passes through two points A(0, -1) and B(4, 1).

Rule for the rotation of any point (x, y), 90° clockwise about the origin is,

(x, y) → (y, -x)

By this rule,

A(0, -1) → A'(-1, 0)

B(4, 1) → B'(1, -4)

Let the equation of the line A'B' is,

y - y' = m(x - x')

where m = slope of the line A'B'

And (x', y') is a point lying on the line.

Slope of the line passing through A' and B' will be,

m = $\frac{y_2-y_1}{x_2-x_1}$

m = $\frac{0+4}{-1-1}$

m = -2

Therefore, equation of the line passing through (-1, 0) and slope = -2,

y - 0 = (-2)(x + 1)

y = -2x - 2

So the equation of the line after rotation of lie 'l' by 90° clockwise will be,

y = -2x - 2

7 0

3 years ago

-

alisha [4.7K]

Answer:

$d=3\sqrt{2}\ units$

Step-by-step explanation:

The complete question is

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)

Find the slope

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

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

substitute the given values

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

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

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

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

$m=-1$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

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