Question

In the rectangular coordinate system, if the line x = 2y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p ?

Answer 1

1

Explanation:

the equation of the line is given as x=2y +5.................................(1)

therefore, 2y=x-5

y=
`(x)/(2)`-
`(5)/(2)`............................................(2)

recall, equation of any line is given as

y=mx + c.......................(3)

where m=slope= y₂ - y₁ / x₂ -x₁...............(4)

∴ by comparison of equations 2 and 3

m=1/2

(x₁,y₁)= (m,n)

(x₂,y₂)=(m+2,n+p)

therefore, from equation 4

`(1)/(2)`=
`(n+p-n)/(m+2-m)`

collecting like terms,

`(1)/(2)`=
`(n-n+p)/(m-m+2)`

`(1)/(2)`=
`(0+p)/(0+2)`

`(1)/(2)`=
`(p)/(2)`

∴p=1

Answer 2

p = 1

Explanation:

Given data:

X = 2y + 5

therefore Y = X/2 - 5/2

Given co-ordinates (m,n) and (m+2,n+p)

Equation of a straight line is represented by Y = mX + C where m is gradient and c is y intercept

For the given equation y intercept is at (0,-5/2) and gradient is 1/2

Given point (X₁ , Y₁) and (X,Y)

Gradient = (Y - Y₁)/(X-X₁)

Finding gradient using (m,n) and (m+2,n+p)

1/2=( n+p - n)/m+2-m)

1/2 = p/2 (Multiplying both sides by 2)

p = 1