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

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.

**Q1: **

At which point do the lines and intersect?

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**Q2: **

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

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**Q3: **

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.

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**Q4: **

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

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**Q5: **

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 .

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**Q6: **

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

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**Q7: **

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

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**Q8: **

Find the equation of the line perpendicular to and passing through the intersection of the lines and .

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**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 .

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**Q10: **

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.

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