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Mathematics, 19.10.2019 20:50 jennkoga

Someone m 75 points to the person that

1. indicate the equation of the given line in standard form.

the line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).

2. indicate the equation of the given line in standard form.

the line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).

3. indicate the equation of the given line in standard form.

the line containing the midpoints of the legs of right triangle abc where a(-5, 5), b(1, 1), and c(3, 4) are the vertices.

4. indicate the equation of the given line in standard form.

the line containing the hypotenuse of right triangle abc where a(-5, 5), b(1, 1), and c(3, 4) are the vertices.

5. indicate the equation of the given line in standard form.

the line containing the longer diagonal of a quadrilateral whose vertices are a (2, 2), b(-2, -2), c(1, -1), and d(6, 4).

6. indicate the equation of the given line in standard form.

the line containing the median of the trapezoid whose vertices are r(-1, 5) , s(1, 8), t(7, -2), and u(2, 0).

7. indicate the equation of the given line in standard form.

the line containing the altitude to the hypotenuse of a right triangle whose vertices are p(-1, 1), q(3, 5), and r(5, -5).

8. indicate the equation of the given line in standard form.

the line containing the diagonal of a square whose vertices are a(-3, 3), b(3, 3), c(3, -3), and d(-3, -3). find two equations, one for each diagonal.

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Answer from: xemnas1994

Part 1) 9x-7y=-25

Part 2) 2x-y=2

Part 3) x+8y=22

Part 4) x+8y=35

Part 5) 3x-4y=2

Part 6) 10x+6y=39

Part 7) x-5y=-6

Part 8)

case A) The equation of the diagonal AC is x+y=0

case B) The equation of the diagonal BD is x-y=0

Step-by-step explanation:

Part 1)

step 1

Find the midpoint

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

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

substitute the values

$M=(\frac{2-6}{2},\frac{-3+5}{2})$

M=(-2,1)

step 2

The equation of the line into point slope form is equal to

$y-1=\frac{9}{7}(x+2)\\ \\y=\frac{9}{7}x+\frac{18}{7}+1\\ \\y=\frac{9}{7}x+\frac{25}{7}$

step 3

Convert to standard form

Remember that the equation of the line into standard form is equal to

Ax+By=C

where

A is a positive integer, and B, and C are integers

$y=\frac{9}{7}x+\frac{25}{7}$

Multiply by 7 both sides

7y=9x+25

9x-7y=-25

Part 2)

step 1

Find the midpoint

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

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

substitute the values

$M=(\frac{1+5}{2},\frac{0-2}{2})$

M=(3,-1)

step 2

Find the slope

The slope between two points is equal to

$m=\frac{-2-0}{5-1}=-\frac{1}{2}$

step 3

we know that

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

Find the slope of the line perpendicular to the segment joining the given points

$m1=-\frac{1}{2}$

m1*m2=-1

therefore

m2=2

step 4

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

m=2 and point (1,0)

$y-0=2(x-1)\\ \\y=2x-2$

step 5

Convert to standard form

Remember that the equation of the line into standard form is equal to

Ax+By=C

where

A is a positive integer, and B, and C are integers

y=2x-2

2x-y=2

Part 3)

In this problem AB and BC are the legs of the right triangle (plot the figure)

step 1

Find the midpoint AB

$M1=(\frac{-5+1}{2},\frac{5+1}{2})$

M1=(-2,3)

step 2

Find the midpoint BC

$M2=(\frac{1+3}{2},\frac{1+4}{2})$

M2=(2,2.5)

step 3

Find the slope M1M2

The slope between two points is equal to

$m=\frac{2.5-3}{2+2}=-\frac{1}{8}$

step 4

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

$m=-\frac{1}{8}$ and point (-2,3)

$y-3=-\frac{1}{8}(x+2)\\ \\y=-\frac{1}{8}x-\frac{1}{4}+3\\ \\y=-\frac{1}{8}x+\frac{11}{4}$

step 5

Convert to standard form

Remember that the equation of the line into standard form is equal to

Ax+By=C

where

A is a positive integer, and B, and C are integers

$y=-\frac{1}{8}x+\frac{11}{4}$

Multiply by 8 both sides

8y=-x+22

x+8y=22

Part 4)

In this problem the hypotenuse is AC (plot the figure)

step 1

Find the slope AC

The slope between two points is equal to

$m=\frac{4-5}{3+5}=-\frac{1}{8}$

step 2

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

$m=-\frac{1}{8}$ and point (3,4)

$y-4=-\frac{1}{8}(x-3)$

$y=-\frac{1}{8}x+\frac{3}{8}+4$

$y=-\frac{1}{8}x+\frac{35}{8}$

step 3

Convert to standard form

Remember that the equation of the line into standard form is equal to

Ax+By=C

where

A is a positive integer, and B, and C are integers

$y=-\frac{1}{8}x+\frac{35}{8}$

Multiply by 8 both sides

8y=-x+35

x+8y=35

Part 5)

The longer diagonal is the segment BD (plot the figure)

step 1

Find the slope BD

The slope between two points is equal to

$m=\frac{4+2}{6+2}=\frac{3}{4}$

step 2

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

$m=\frac{3}{4}$ and point (-2,-2)

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

$y=\frac{3}{4}x+\frac{6}{4}-2$

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

step 3

Convert to standard form

Remember that the equation of the line into standard form is equal to

Ax+By=C

where

A is a positive integer, and B, and C are integers

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

Multiply by 4 both sides

4y=3x-2

3x-4y=2

Note The complete answers in the attached file

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Answer from: Quest

i can't read the graph

step-by-step explanation:

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Answer from: Quest

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