Problem Help Flag 2 M 15 is the midpoint of RS IfS has coord

Problem Help Flag 2. M (-1,-5) is the midpoint of RS. IfS has coordinates (7,-3), find the coordinates of R o (15-7) (15, -1) (-9-7) (-9 -1) (15, -7

Solution

2) Given Points R ans S.

R=(7,-3) Let s be (x,y)

Mid point of RS is M(-1,-5)

mid point is the average of two points.

So, (7+x)/2 = -1 and (-3+y)/2 = -5

7+x=-2 -3+y=-10

x=-2-7 y=-10+3

x=-9 y=-7

Therefore, S is (-9,-7)

So, option B is correct.

3) Given equation of line is -3x-5y=-10 and a point (2,-1)

equation of line is -3x-5y=-10

It can be taken in slope intercept form.

-3x-5y=-10

5y=-3x+10

y=(-3/5)x+(10/5)

y=(-3/5)x+2

So, slope is -3/5,

The line perpendicular to this -3x-5y=-10 line has slope of 5/3.

General slope intercept form can be taken as y=mx+c

y=(5/3)x+c

3y=5x+3c

This line passes through the point (2,-1)

3y=5x+3c

substitute (2,-1) in the above to get c

3(-1) = 5(2)+3c

-3 = 10+3c

3c=-3-10

3c=-13

The equation of a line is 3y=5x+3c

3y=5x+(-13)

3y=5x-13

5x-3y=13

Therefore the equation of a line perpendicular to -3x-5y=-10 and passing through (2,-1) is 5x-3y=13

So, option A is correct.

4) Given equation is y=3x+4 and a point (5,-2)

Need to find the line parallel to y=3x+4 and passing through the (5,-2)

Slope of y=3x+4 is \'3\' because it is in Slope intercept form y=mx+c where m-slope

The required line has the slope \'3\' because required line is parallel to given line.

So, required line is y=3x+c

This line passes through the point (5,-2)

y=3x+c

-2=3(5)+c

-2=15+c

c=-2-15

c=-17

The required line is y=3x+c

y=3x-17

Therefore, Option B is correct.