# 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.

Q1:

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

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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.

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Q3:

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

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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 .

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Q5:

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

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Q6:

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

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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 .

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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 .

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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:

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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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.

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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.

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Q14:

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

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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.

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Q16:

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

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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.

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Q18:

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

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Q19:

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

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Q20:

At which point do the lines and intersect?

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Q21:

Find the intersection point of the two straight lines and .

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Q22:

Find the intersection of the lines and .

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Q23:

At which point do the lines and intersect?

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Q24:

Where do the straight lines and intersect?