# Worksheet: Intersection Point of Two Straight Lines on the Coordinate Plane

In this worksheet, we will practice finding the intersection point between two straight lines on a coordinate system and using this concept to find equations of lines.

**Q2: **

Determine the equation of the line passing through the point of intersection of the two lines whose equations are and while making an angle of with the positive -axis.

- A
- B
- C
- D

**Q3: **

Find the equation of the straight line that passes through the origin and the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q4: **

Find the equation of the straight line that is parallel to the -axis and passes through the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q5: **

What is the equation of the line passing through and the intersection of the lines and ?

- A
- B
- C

**Q7: **

Find the equation of the straight line which passes through the point of intersection of the two lines and and is parallel to the straight line .

- A
- B
- C
- D

**Q8: **

Find the equation of the straight line which passes through the point of intersection of the two lines and and is parallel to the straight line .

- A
- B
- C
- D

**Q9: **

Find the vector equation of the straight line that is parallel to the -axis and passes through the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q10: **

Find the vector equation of the straight line that passes through the point of intersection of the two straight lines and and the point .

- A
- B
- C
- D

**Q11: **

Find the -coordinate of the point at which the straight line cuts the -axis.

**Q12: **

The lines and intersect orthogonally. Find the coordinates of the point of intersection.

- A
- B
- C
- D

**Q13: **

Find the equation of the straight line that passes through the point of intersection of the two lines and , given that it is perpendicular to the second line.

- A
- B
- C
- D

**Q14: **

Find the point of intersection of the two straight lines and .

- A
- B
- C
- D

**Q15: **

Find the equation of the straight line that passes through the point of intersection of the two straight lines and and intersects the negative direction of the -axis at a point that is 10 length units away from the origin.

- A
- B
- C
- D

**Q16: **

Determine the point of intersection of the two straight lines represented by the equations and .

- A
- B
- C
- D

**Q17: **

Find the equation of the straight line, passing through the point of intersection of the two straight lines and , that intersects the positive directions of the coordinate axes in two points at the same distance from the origin.

- A
- B
- C
- D

**Q18: **

What is the equation of the line passing through and the intersection of the lines and ?

- A
- B
- C

**Q19: **

Find the coordinates of the intersection point between a straight line represented by the equation and the -axis.

- A
- B
- C
- D
- E

**Q20: **

At which point do the lines and intersect?

- A
- B
- C
- D

**Q21: **

Find the intersection point of the two straight lines and .

- A
- B
- C
- D
- E

**Q22: **

Find the intersection of the lines and .

- A
- B
- C
- D
- E

**Q23: **

At which point do the lines and intersect?

- A
- B
- C
- D
- E

**Q24: **

Where do the straight lines and intersect?

- Athird quadrant
- Bfirst quadrant
- Csecond quadrant
- Dfourth quadrant
- Eorigin

**Q25: **

The coordinates of the points and are and respectively. Given that intersects the -axis at and the -axis at , determine the coordinates of and .

- A,
- B,
- C,
- D,