Straight Line

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What is the equation of the bisector of the acute angle between the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0?

3x + 4y - 7 = 0

21x + 77y - 101 = 0

12x - 5y + 2 = 0

11x - 3y + 9 = 0 (correct)

What is the length of the perpendicular from the origin to the line ax + by + c = 0?

x1 cos α + y1 sin α - p

|ax1 + by1 + c| / √(a^2 + b^2) (correct)

α / (a^2 + b^2)

√(a^2 + b^2)

What is the distance of a point (x1, y1) from the line ax + by + c = 0?

x1 cos α + y1 sin α - p

|ax1 + by1 + c| / √(a^2 + b^2) (correct)

√(a^2 + b^2)

α / (a^2 + b^2)

What is the equation of two parallel lines?

ax + by + c1 = 0 and ax + by + c2 = 0 Signup and view all the answers

What is the slope of a line perpendicular to the line 3x - 4y + 7 = 0?

-4/3 Signup and view all the answers

What is the slope of a line parallel to the x-axis?

0 Signup and view all the answers

What is the condition for two lines to be parallel?

Slopes are equal Signup and view all the answers

What is the slope of a line that is equally inclined with the axes?

1 or -1 Signup and view all the answers

How many points determine a unique line?

Two Signup and view all the answers

What is the slope of a line perpendicular to another line with a slope of 2?

-1/2 Signup and view all the answers

What is the equation of the line bisecting perpendicularly the segment joining the points (–4, 6) and (8, 8)?

6x + y - 19 = 0 Signup and view all the answers

What is the slope of the line passing through (–4, 6) and (8, 8)?

1/4 Signup and view all the answers

What is the midpoint of the line segment joining the points (–4, 6) and (8, 8)?

(2, 7) Signup and view all the answers

What is the equation of a line parallel to the line passing through (–4, 6) and (8, 8)?

y - 7 = 1/4(x - 2) Signup and view all the answers

What is the equation of a line perpendicular to the line passing through (–4, 6) and (8, 8)?

x + 4y - 7 = 0 Signup and view all the answers

If a line passes through the points (–4, 6) and (8, 8), what is the equation of a line perpendicular to it?

6x – 2y + 19 = 0 Signup and view all the answers

What is the midpoint of the line segment joining the points (5, 3) and (9, 11)?

(7, 7) Signup and view all the answers

If two lines have slopes of 3/4 and –4/3, what can be said about the lines?

They are perpendicular Signup and view all the answers

What is the equation of a line that passes through the point (3, 4) and is parallel to the line 2x + 3y – 7 = 0?

2x + 3y + 5 = 0 Signup and view all the answers

What is the slope of a line that is perpendicular to the line x + 2y – 5 = 0?

1/–2 Signup and view all the answers

If the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 are intersecting, what is the tangent of the angle between them?

13/35 Signup and view all the answers

What is the equation of the line parallel to the line 3x - 4y + 7 = 0 and passing through the point (1, 1)?

3x - 4y - 2 = 0 Signup and view all the answers

If the length of the perpendicular from the origin to the line ax + by + c = 0 is p, what is the value of $\frac{a^2+b^2}{p^2}$?

1 Signup and view all the answers

What is the midpoint of the line segment joining the points (3, 4) and (5, 8)?

(4, 6) Signup and view all the answers

What is the slope of the line perpendicular to the line 3x - 4y + 7 = 0?

-3/4 Signup and view all the answers

If a line passes through the points A(x1, y1) and B(x2, y2), what is the slope of the line?

m = (y2 - y1) / (x2 - x1) Signup and view all the answers

What is the equation of a line perpendicular to the line ax + by + c = 0?

bx - ay + c = 0 Signup and view all the answers

If two lines have slopes m1 and m2, what is the condition for them to be perpendicular?

m1 = -m2 Signup and view all the answers

What is the midpoint of the line segment joining the points (x1, y1) and (x2, y2)?

((x1 + x2)/2, (y1 + y2)/2) Signup and view all the answers

What is the equation of a line parallel to the line ax + by + c = 0?

ax + by + kc = 0, where k is a constant Signup and view all the answers