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.

Part 1)

Part 2)

Part 3)  

Part 4)

Part 5)

Part 6)

Part 7)

Part 8)

case A) The equation of the diagonal AC is

case B) The equation of the diagonal BD is

Step-by-step explanation:

Part 1)

step 1

Find the midpoint

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

substitute the values

step 2

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

step 3

Convert to standard form

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

where

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

Multiply by 7 both sides

Part 2)

step 1

Find the midpoint

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

substitute the values

step 2

Find the slope

The slope between two points is equal to

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

therefore

step 4

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

we have

and point

step 5

Convert to standard form

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

where

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

Part 3)

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

step 1

Find the midpoint AB

step 2

Find the midpoint BC

step 3

Find the slope M1M2

The slope between two points is equal to

step 4

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

we have

and point

step 5

Convert to standard form

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

where

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

Multiply by 8 both sides

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

step 2

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

we have

and point

step 3

Convert to standard form

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

where

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

Multiply by 8 both sides

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

step 2

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

we have

and point

step 3

Convert to standard form

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

where

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

Multiply by 4 both sides

Note The complete answers in the attached file