A is the point (2, 3) and B is the point (7,-5).Find the equation of the linethrough A that is perpendicular to AB. Give your answer in the form y =
mx+C.

Answers

Answer 1

Answer:

The equation of the line that is perpendicular to line AB will be y = (5/8) x + c.

What is the equation of a perpendicular line?

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

A is the point (2, 3) and B is the point (7,-5). Then the slope of the line AB is given as,

m = (3 + 5) / (2 - 7)

m = - 8 / 5

Then the slope of the perpendicular line is given as,

⇒ -1/m

⇒ - 1/(- 8/5)

⇒ 5/8

Then the equation of the perpendicular line is given as,

y = (5/8) x + c

The equation of the line that is perpendicular to line AB will be y = (5/8) x + c.

More about the equation of a perpendicular line link is given below.

brainly.com/question/14200719

#SPJ2

Answer 2

Answer:

Answer:

y=0.625x+1.75

Step-by-step explanation:

The equation of the line that goes through (2, 3) and (7, -5) needs to be found before finding the equation perpendicular to it. The formula y=mx+c will be used for finding this equation.

Calculating the slope between the data points:

$m1=(3-(-5))/(2-7)=(8)/(-5)=-1.6$

Finding the first y-intercept:

$y=mx+c$

$c=y-mx$

$c=3-(-1.6*2)=3+3.2=6.2$

The equation for the line that goes through the points is:

$y=-1.6x+6.2$

The perpendicular slope will be the opposite reciprocal of the original slope.

The second slope is found by first multiplying the first slope (m1) by -1:

$m2=m1*-1=-1.6*-1=1.6$

Then by taking the reciprocal:

$m2=(1)/(1.6) =0.625$

The second equation must have an intercept that goes through point A:

$c=y-mx$

$c=3-(0.625*2)=3-1.25=1.75$

The perpendicular equation is:

$y=0.625x+1.75$

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Answers

Answer:

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Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2. A. (-5, -15) B. (-23, -5) C. (-13, -7) D. (-11.5, -2.5)

Answers

Answer:

C. (-13, -7)

Step-by-step explanation:

The location of a point O(x, y) that divides a line AB with location A $(x_1,y_1)$ and B $(x_2,y_2)$ in the ratio m:n is given by:

$x=(m)/(m+n) (x_2-x_1)+x_1\n\ny=(m)/(m+n) (y_2-y_1)+y_1$

Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:

$x=(5)/(5+2) (-15-(-8))+(-8)\n\nx=(5)/(7) (-15+8)-8=(5)/(7)(-7)-8=-5-8=-13 \n\n\ny=(5)/(5+2) (-13-8)+8\n\ny=(5)/(7) (-21)+8=5(-3)+8=-15+8=-7$

Therefore the coordinates of point X is at (-13, -7)

Cho and Jeff each bought a used bike. Jeff's bike was not on sale and cost the same amount as theoriginal price of Cho's bike. Cho's bike was on sale for $20 less than the original price, and her total
cost was half of what Jeff paid. How much money did Jeff pay for his bike?
A. $30
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C. $20
D. $40

Answers

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