RD Chapter 23 The Straight Lines Ex 23.2 Solutions
Question - 1 : - Find the equation of the parallel to x–axis and passing through (3, –5).
Answer - 1 : -
Given: A line which isparallel to x–axis and passing through (3, –5)
By using the formula,
The equation of line:[y – y1 = m(x – x1)]
We know that theparallel lines have equal slopes
And, the slope ofx–axis is always 0
Then
The slope of line, m =0
Coordinates of lineare (x1, y1) = (3, –5)
The equation of line =y – y1 = m(x – x1)
Now, substitute thevalues, we get
y – (– 5) = 0(x – 3)
y + 5 = 0
∴ The equation of lineis y + 5 = 0
Question - 2 : - Find the equation of the line perpendicular to x–axis and having intercept – 2 on x–axis.
Answer - 2 : -
Given: A line which isperpendicular to x–axis and having intercept –2
By using the formula,
The equation of line:[y – y1 = m(x – x1)]
We know that, the lineis perpendicular to the x–axis, then x is 0 and y is –1.
The slope of line is,m = y/x
= -1/0
It is given thatx–intercept is –2, so, y is 0.
Coordinates of lineare (x1, y1) = (–2, 0)
The equation of line =y – y1 = m(x – x1)
Now, substitute thevalues, we get
y – 0= (-1/0) (x – (– 2))
x + 2 = 0
∴ The equation of lineis x + 2 = 0
Question - 3 : - Find the equation of the line parallel to x–axis and having intercept – 2 on y – axis.
Answer - 3 : -
Given: A line which isparallel to x–axis and having intercept –2 on y – axis
By using the formula,
The equation of line:[y – y1 = m(x – x1)]
The parallel lineshave equal slopes,
And, the slope ofx–axis is always 0
Then
The slope of line, m =0
It is given thatintercept is –2, on y – axis then
Coordinates of lineare (x1, y1) = (0, – 2)
The equation of lineis y – y1 = m(x – x1)
Now, substitute thevalues, we get
y – (– 2) = 0 (x – 0)
y + 2 = 0
∴ The equation of lineis y + 2 = 0
Question - 4 : - Draw the lines x = –3, x = 2, y = –2, y = 3 and write the coordinates of the vertices of the square so formed.
Answer - 4 : -
Given: x = –3, x = 2,y = –2 and y = 3
∴ The Coordinates ofthe square are: A(2, 3), B(2, –2), C(–3, 3), and D(–3, –2).
Question - 5 : - Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x–axis.
Answer - 5 : -
Given: A line which isperpendicular and parallel to x–axis respectively and passing through (4, 3)
By using the formula,
The equation of line:[y – y1 = m(x – x1)]
Let us consider,
Case 1: When Line isparallel to x–axis
The parallel lineshave equal slopes,
And, the slope ofx–axis is always 0, then
The slope of line, m =0
Coordinates of lineare (x1, y1) = (4, 3)
The equation of lineis y – y1 = m(x – x1)
Now substitute thevalues, we get
y – (3) = 0(x – 4)
y – 3 = 0
Case 2: When line isperpendicular to x–axis
The line isperpendicular to the x–axis, then x is 0 and y is – 1.
The slope of the lineis, m = y/x
= -1/0
Coordinates of lineare (x1, y1) = (4, 3)
The equation of line =y – y1 = m(x – x1)
Now substitute the values,we get
y – 3 = (-1/0) (x – 4)
x = 4
∴ The equation of linewhen it is parallel to x – axis is y = 3 and it is perpendicular is x = 4.