Problem Solving

In a rectangular co-ordinate system ,if a line pass through the points (-1o,-18 ) (20,22)and (x,2),what is the value of x ?

Md.Nazrul Islam wrote:In a rectangular co-ordinate system ,if a line pass through the points (-1o,-18 ) (20,22)and (x,2),what is the value of x ?

You need to make an equation line here. Start with finding a slope, (22-{-18})/(20-{-10})=(22+18)/(20+10)=4/3. Then find y-intercept and for this plug in one coordinate into y=mx+b where m is slope (just found), for example the coordinate (20,22) will be enough --> 22=(4/3)*20 + b and b=22-80/3=-14/3. Our line equation will be y=(4/3)x-14/3. Now, test the coordinate (x,2) and find x --> y=2 and 2=(4/3)x-14/3, 4x/3=2+14/3, 4x=6+14 and x=5.

answer [spoiler]x=5[/spoiler]

(20-(-10))/22-(-18) = (20-x)/22-2
30/40 = (20-x)/20
15=20-x
x=5

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we will find the equation of the line passing through (-10, -18) and (20, 22).
The slope = (22-(-18))/(20-(-10))= 40/30
so, slope = 4/3

the line's equation is: y-(-18) = (4/3)*(x-(-10))
y +18 = (4/3)*(x+10)

this line passes through (x, 2). Hence we will plug in y = 2 and find x.

2+18=(4/3)*(x+10)
20 = (4/3)*(x+10)
15 = x+10
==> x = 5

The x coordinate is 5.

The eq of st line passing thru 2 points is (x-x1)/(y-y1) = ((x2-x1)/(y2-y1)
Eq is thus 4x-3y-14 = 0
y = 2 => x = 5