Math, asked by Keshav7643, 1 month ago

if the slope of the line joining the points (x,5) and (-1,2) is 3/4.Find the value of x. Also determine the distance between them.

Answers

Answered by tennetiraj86
2

Step-by-step explanation:

Given :-

The slope of the line joining the points (x,5) and (-1,2) is 3/4.

To find :-

i) Find the value of x.

ii) Determine the distance between them.

Solution:-

Given points are (x,5) and (-1,2)

Let (x1, y1)=(x,5)=>x1 = x and y1 = 5

Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2

We know that

The slope of a linesegment joining the points

(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)

On Substituting these values in the above formula

=> Slope = (2-5)/(-1-x)

=> Slope = -3/(-1-x)

=> Slope = -3/-(1+x)

=> Slope = 3/(1+x)

According to the given problem

The slope = 3/4

=> 3/(1+x) = 3/4

=> 1/(1+x) = 1/4

=>1+x = 4

=> x = 4-1

=> x = 3

Therefore, x = 3

Now the points are (3,5) and (-1,2)

We know that

The distance between two points (x1, y1) and

(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units

Let (x1, y1)=(3,5)=>x1 = 3 and y1 = 5

Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2

Distance = √[(-1-3)^2+(2-5)^2]

=> √[(-4)^2+(-3)^2]

=> √(16+9)

=> √25

=> 5 units

Answer:-

The value of x for the given problem is 3

The distance between the two points is 5 units

Used formulae:-

Slope :-

The slope of a linesegment joining the points

(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)

Distance formula:

The distance between two points (x1, y1) and

(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units

Answered by tarunkiranp
0

Given :-

The slope of the line joining the points (x,5) and (-1,2) is 3/4.

To find :-

i) Find the value of x.

ii) Determine the distance between them.

Solution:-

Given points are (x,5) and (-1,2)

Let (x1, y1)=(x,5)=>x1 = x and y1 = 5

Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2

We know that

The slope of a linesegment joining the points

(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)

On Substituting these values in the above formula

=> Slope = (2-5)/(-1-x)

=> Slope = -3/(-1-x)

=> Slope = -3/-(1+x)

=> Slope = 3/(1+x)

According to the given problem

The slope = 3/4

=> 3/(1+x) = 3/4

=> 1/(1+x) = 1/4

=>1+x = 4

=> x = 4-1

=> x = 3

Therefore, x = 3

Now the points are (3,5) and (-1,2)

We know that

The distance between two points (x1, y1) and

(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units

Let (x1, y1)=(3,5)=>x1 = 3 and y1 = 5

Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2

Distance = √[(-1-3)^2+(2-5)^2]

=> √[(-4)^2+(-3)^2]

=> √(16+9)

=> √25

=> 5 units

Answer:-

The value of x for the given problem is 3

The distance between the two points is 5 units

Used formulae:-

Slope :-

The slope of a linesegment joining the points

(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)

Distance formula:

The distance between two points (x1, y1) and

(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units

I HOPE IT WILL HELPFUL TO YOU

Similar questions