Find Missing Coordinate Using Slope

FIND A MISSING COORDINATE USING Gradient

Instance 1 :

The slope of a line is iii/2 and the line contains the points (5, 9) and (3, a). What is the value of a ?

Solution :

Formula to detect the slope of a line when ii points are given :

m  =  (y₂ - y₁) / (x_ii - ten₁)

Given : Slope of the line is three/2.

And so,

(y₂ - y₁) / (x₂ - x₁)  =  3/2

Substitute (x₁, y_ane) = (5, 9) and (x₂, y_ii) = (3, a).

(a - 9) / (3 - 5)  =  3/2

(a - 9) / (-2)  =  iii/2

Multiply each side by (-ii).

a - 9  =  -3

Add 9 to each side.

a  =  6

Example 2 :

The slope of a line is -ii and the line contains the points (7 , 4) and (x, 12). What is the value of x ?

Solution :

Formula to observe the slope of a line when ii points are given :

m  =  (y₂ - y₁) / (x₂ - x₁)

Given :  Gradient of the line is -2.

And then,

(y₂ - y₁) / (ten₂ - x_one)  =  -two

Substitute (x₁, y₁) = (vii, 4) and (x_ii, y₂) = (ten, 12).

(12 - 4) / (x - 7)  =  -2

8 / (x - 7)  =  -ii

Take reciprocal on each side.

(ten - 7) / 8  =  -1/two

Multiply each side by 8.

x - 7  =  -4

Add together 7 to each side.

10  =  3

Instance 3 :

The slope of a line is two/t and the line contains the points (-2 ,4) and (-vi, ten). What is the value of t?

Solution :

Formula to notice the slope of a line when two points are given :

1000  =  (y₂ - y_i) / (x₂ - x₁)

Given :  Slope of the line is 2/t.

Then,

(y₂ - y₁) / (10₂ - x₁)  =  2/t

Substitute (10₁, y₁) = (-two, 4) and (x₂, y₂) = (-half-dozen, ten).

(10 - 4) / (-vi + two)  =  two/t

half dozen / (-4)  =  2/t

-3/2  =  2/t

Take reciprocal on each side.

-2/3  =  t/2

Multiply each side by 2.

-4/3  =  t

Example four :

The line through the points (-2, a) and (ix, iii) has gradient -1/ two . Find the value of a.

Solution :

Formula to find the slope of a line when two points are given :

1000  =  (y_ii - y₁) / (x_ii - x_i)

Given :  Slope of the line is -one/2.

And then,

(y₂ - y₁) / (x₂ - ten₁)  =  ii/t

Substitute (ten₁, y₁) = (-2, a) and (x₂, y_two) = (9, 3).

(3 - a) / (9 + 2)  =  -1/2

(3 - a) / 11  =  -ane/two

Multiply each side by 11.

3 - a  =  -11/2

Subtract 3 from each side.

-a  =  -xi/2 - 3

-a  =  -11/two - 6/ii

-a  =  (-11 - 6) / 2

-a  =  -17/ii

Multiply each side by (-i).

a  =  17/2

Case 5 :

The line through the points (-ii, half-dozen) and (4, viii) is perpendicular to the line through the points (eight, 12) and (x, 24) . Find the value of x.

Solution :

Slope of the line joining (-2, 6) and (4, 8) :

m  =  (8 - half dozen)/(4 - (-2))

  =  2 / (4 + 2)

  =  2/six

  =  ane/3 -----(i)

Slope of the line joining (eight, 12) and (ten, 24) .

1000  =  (24 - 12)/(10 - 8)

  =  12/(x - viii) -----(ii)

if lines are perpendicular to each other, the product of the slopes is equal to -1.

So,

(1/3) ⋅ 12/(10 - viii) =  -ane

4/(x - 8)  =  -one

4  =  -(10 - 8)

4  =  -x + eight

x  =  8 - 4

x  =  4

Apart from the stuff given above, if you need any other stuff in math, delight apply our google custom search here.

Kindly mail your feedback tov4formath@gmail.com

We e'er capeesh your feedback.

© All rights reserved. onlinemath4all.com

Find Missing Coordinate Using Slope,

Source: https://www.onlinemath4all.com/find-a-missing-coordinate-using-slope.html

Posted by: burgessnatch1943.blogspot.com

Share this post