You visited us 1 times! Enjoying our articles? Unlock Full Access!

Distance Time Graph

In the x-y ...

Question

In the $x - y$ plane, the lines $y = 2 x - 1$ and $y = x + c$ intersect at point $P$ , where $c$ is a positive number. Portions of these lines are shown in the figure above. If the value of $c$ is between $1$ and $2$ , find the one possible value of the $x$ -coordinate of $P$ .

2 < x < 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5 < x < 7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

11 < x < 12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 < x < 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7 < x < 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 < x < 3$
As given, $y = x + c$ , $y = 2 x - 1$
To determine at what point the two lines intersect, set the equations of the lines equal to one another.
i.e: $x + c = 2 x - 1$
So, $x = c + 1$ it represents the the $x$ -coordinate of $P$ , the point where the two lines intersect.
Now as per question, if $C$ is between $1$ and $2$ , then the C $+$ 1 will be in between $2$ and $3$ .
Therefore, the one possible value of the $x$ -coordinate of $P$ can be any value between $2$ and $3$ .
Hence, option A is correct.

Suggest Corrections

Similar questions

Q. The straight lines

3 x + 4 y = 5

and

4 x - 3 y = 15

intersect at the point

A

. On these lines points

B

and

C

are chosen so that

A B = A C

.Possible equation(s) of the line

B C

passing through

(1, 2)

is/are

Q. Question 4 (iii)
Find the value(s) of p for the following pair of equations – 3x + 5y = 7 and 2px – 3y = 1,
If the lines represented by these equations are intersecting at a unique point.

If the lines $\frac{1 - x}{3} = \frac{7 y - 14}{2 p} = \frac{z - 3}{2} a n d \frac{7 - 7 x}{3 p} = \frac{y - x}{1} = \frac{6 - z}{5} =$ and are at right angle, then the value of is

Q. Find the value of

p

so that the lines

\frac{x + 1}{- 3} = \frac{y - p}{2} = \frac{z + 2}{1}

and

\frac{x}{1} = \frac{y - 7}{- 3} = \frac{z + 7}{2}

are in the same plane.

Q. Straight lines

x - y = 7

and

x + 4 y = 2

intersect at B. Points A and C are so chosen on these two lines such that AB = AC. The equation of line AC passing through (2, –7) is

Join BYJU'S Learning Program

In the x−y plane, the lines y=2x−1 and y=x+c intersect at point P, where c is a positive number. Portions of these lines are shown in the figure above. If the value of c is between 1 and 2, find the one possible value of the x-coordinate of P.

In the $x - y$ plane, the lines $y = 2 x - 1$ and $y = x + c$ intersect at point $P$ , where $c$ is a positive number. Portions of these lines are shown in the figure above. If the value of $c$ is between $1$ and $2$ , find the one possible value of the $x$ -coordinate of $P$ .