Question

CD is formed by C(-5, 9) and D(7,5). If line
t is the perpendicular bisector of CD, write a
linear equation for t in slope-intercept form

Answer 1

Answer:

y - 3x = 10

Step-by-step explanation:

The equation of a line in slope-intercept form is expressed as;

y - y0 = m(x-x0) where;

m is the slope of the unknown line

(x0, y0) is any point on the line.

First is to get the slope.

Given CD is formed by C(-5, 9) and D(7,5)

m  = y2-y1/x2-x1

m = 5-9/7+5

m = -4/12

m = -1/3

Since the line t is perpendicular to CD, the product of their slope will be -1.

mM = -1

M = -1/(-1/3)

M = 3

Substituting M = 3 and the midpoint of (7, 5) and (-5, 9 )into the formula above to get the equation of the line.

Midpoint of the line = (x1+x2/2, y1+y2/2)

M = (-7+5/2, 5+9/2)

M = (-2/2, 14/2)

M = (-1, 7)

Hence x0 = -1 and y0 = 7

Since y - y0 = m(x-x0

Equation becomes;

y-7 = 3(x+1)

y-7 = 3x+3

y-3x = 3+7

y - 3x = 10

Hence  a  linear equation for t in slope-intercept form is y-3x = 10

Answer 2

The Equation of perpendicular bisector t = $y = 3x +4$

Given Line CD is formed by points  C(-5, 9) and D(7,5) hence it passes through these two points

Let the slope of this line is m

The Slope of line passing through C and D points is given by $m$

So

$m = (y_2-y_1) /(x_2-x_1)$.....(1)

$m = (5-9)/(7-(-5)) = -1/3.......(2)$

Given that $t$ is perpendicular bisector of CD

Let the slope of t  = $m_t$

The product of  slopes of two perpendicular lines is -1

hence

$m \times m_t = -1........(3)$

so we can from equation number (2) and (3) we can write

$m_t$ = 3

Also t is the perpendicular bisector and hence it passes through the mid point of line CD hence the mid point of CD

$Midpoint \; of\; line \; joining\; two\; points = ((x_1+ x_2)/2, (y_1+y_2)/2) .......(4)$

From equation 4 we can write that

Mid point of CD =

$((-5 +7)/2, ( 9 +5)/2 ) = (1,7)$

The equation of perpendicular bisector t  is given by equation (5)

$y = 3x+c .........(5)$

also equation (5) is satisfied by the point (1,7)

hence we can write

$7 = 3\times (1) +c \\ c = 4$

So  the Equation of perpendicular bisector t = $y = 3x +4$

For more information refer to the link given below

https://brainly.com/question/24753075