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3 years ago

HELP PICTURE IS INCLUDEDWhat transformations were applied to ABCD to obtain A'B'C'D'?

Mathematics

1 answer:

Liula [17]3 years ago

4 0

In the figure ABCD is transformed to figure A'B'C'D'. It is Transformed from Quadrant 1 to quadrant 2 .That is point (x,y) is (-y,x) It is then moved up by 2 units.The figure ABCD is rotated counterclockwise and then translated up by 2 units to come to A'B'C'D'.

Option b Rotate 90 degrees counterclockwise then translate 2 units up is the right answer.

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Answer:

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3 years ago

A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:

Dima020 [189]

Answer:

Part A) $y=\frac{3}{4}x-\frac{1}{4}$

Part B) $y=\frac{2}{7}x-\frac{5}{7}$

Part C) $y=\frac{2}{7}x+\frac{8}{7}$

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

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

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment NM

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

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

we have

N(3, 2) and M(-1,-1)

substitute the values

$m=\frac{-1-2}{-1-3}$

$m=\frac{-3}{-4}$

$m=\frac{3}{4}$

step 3

Find the equation of the line in point slope form

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

we have

$m=\frac{3}{4}$

$point\ N(3, 2)$

substitute

$y-2=\frac{3}{4}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{3}{4}x-\frac{9}{4}$

$y=\frac{3}{4}x-\frac{9}{4}+2$

$y=\frac{3}{4}x-\frac{1}{4}$

Part B) Find the equation of the right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

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

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 4

Find the equation of the line in point slope form

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

we have

$m=\frac{2}{7}$

$point\ M(-1,-1)$ ----> midpoint LP

substitute

$y+1=\frac{2}{7}(x+1)$

step 5

Convert to slope intercept form

Isolate the variable y

$y+1=\frac{2}{7}x+\frac{2}{7}$

$y=\frac{2}{7}x+\frac{2}{7}-1$

$y=\frac{2}{7}x-\frac{5}{7}$

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 3

Find the equation of the line in point slope form

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

we have

$m=\frac{2}{7}$

$point\ N(3,2)$

substitute

$y-2=\frac{2}{7}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{2}{7}x-\frac{6}{7}$

$y=\frac{2}{7}x-\frac{6}{7}+2$

$y=\frac{2}{7}x+\frac{8}{7}$

7 0

3 years ago

Plot point C(2,7). If M is the midpoint of CD , what are the coordinates of D?

Y_Kistochka [10]

Answer:

The coordinates of D is (-4,-9)

Step-by-step explanation:

Given

C = (2,7)

M=(-1,-1) ----- Missing part of question

Required

Determine the coordinates of D

Let the coordinates of D be (x₂,y₂)

We'll solve this question using mid point formula;

$M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where

$C(x_1,y_1) = (2,7)$ and $M(x,y) = (-1,-1)$

Put these values in the formula

$(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})$

By comparison;

$-1 = \frac{2+x_2}{2}$ and $-1 = \frac{7+y_2}{2}$

$-1 = \frac{2+x_2}{2}$

Multiply both sides by 2

$-2 = 2 + x_2$

Subtract 2 from both sides

$-2 -2 = x_2$

$x_2 = -4$

$-1 = \frac{7+y_2}{2}$

Multiply both sides by 2

$-2 = 7 + y_2$

Subtract 7 from both sides

$-2 - 7 = y_2$

$y_2 = -9$

Hence, the coordinates of D is (-4,-9)

4 0

3 years ago

9. Put these numbers in greatest to least order: 2/3, 60%, 0.06, 3/4

Iteru [2.4K]

Step-by-step explanation:

0.06
60%
2/3
3/4

hope it's right :)

8 0

3 years ago

Mary works in a factory that produces 1000 computers each day. When 25 computers were sampled, 7 were found to be defective. Est

harkovskaia [24]

Answer:

the correct is D. 280

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers