Analytic Geometry and Linear Equations Quiz

Test your knowledge on equations of lines, planes, matrices, and vectors in analytic geometry. Includes slope-intercept, standard, parametric forms, determinants, eigenvalues, and intersections.

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Which of the following is the equation of a line in slope-intercept form?

y = mx + b

Ax + By = C

x = a

y = a/x

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

Undefined

Any real number

What is the distance between two points (x1, y1) and (x2, y2) in the coordinate plane?

sqrt((x2 - x1)^2 + (y2 - y1)^2)

(x2 - x1) + (y2 - y1)

sqrt((x2 + x1)^2 + (y2 + y1)^2)

(x2 + x1) + (y2 + y1)

What is the equation of a plane in three-dimensional space?

Ax + By = C

z = mx + ny + p

Ax + By + Cz = D

x = a

What is the equation of a line perpendicular to y = 3x + 2 and passing through the point (2, -1)?

y = 3x + 2

y = -1/3x - 2

y = -3x + 8

y = 1/3x + 2

In parametric form, what are the coordinates of a point on a line given by x = 2t - 1 and y = 3t + 4?

(2, 3)

(-1, 4)

(3, 4)

(1, 2)

What is the standard form of the equation of a circle with center (h, k) and radius r?

(x - h)^2 + (y - k)^2 = r

y = mx + b

Ax + By = C

x = a

In the matrix equation AX = B, what does matrix A represent?

Coefficients

Variables

Solutions

Constants

What is the determinant of a 2x2 matrix [[a, b], [c, d]]?

ad - bc

a + d

a - d

bd - ac

#10

Which conic section is described by the equation Ax^2 + By^2 = C?

Ellipse

Hyperbola

Parabola

Circle

#11

What is the intersection point of the lines x - y = 3 and 2x + y = 1?

(-1, -4)

(4, 1)

(1, -2)

(2, 1)

#12

What is the equation of the line of reflection for the line y = 2x + 5?

y = -2x - 5

y = -2x + 5

y = 2x - 5

y = 2x + 5

#13

What is the eigenvalue of a matrix?

A real number associated with the matrix

A vector in the matrix

The determinant of the matrix

The rank of the matrix

#14

What is the condition for three points to be collinear in the coordinate plane?

They have the same x-coordinates

They have the same y-coordinates

The slope between any two points is the same

The sum of the x-coordinates equals the sum of the y-coordinates

#15

If two lines are parallel, what can be said about their slopes?

They have the same slope

Their slopes are negative reciprocals

Their slopes add up to zero

Their slopes multiply to give -1

#16

What is the equation of the sphere with center (h, k, l) and radius r?

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

x^2 + y^2 + z^2 = r

Ax + By + Cz = D

z = mx + ny + p

#17

What is the cross product of vectors A = <1, 2, 3> and B = <4, 5, 6>?

<3, -6, 3>

<3, -3, -6>

<-3, 6, -3>

<-3, -3, 6>

Analytic Geometry and Linear Equations Quiz

Which of the following is the equation of a line in slope-intercept form?

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

What is the distance between two points (x1, y1) and (x2, y2) in the coordinate plane?

What is the equation of a plane in three-dimensional space?

What is the equation of a line perpendicular to y = 3x + 2 and passing through the point (2, -1)?

In parametric form, what are the coordinates of a point on a line given by x = 2t - 1 and y = 3t + 4?

What is the standard form of the equation of a circle with center (h, k) and radius r?

In the matrix equation AX = B, what does matrix A represent?

What is the determinant of a 2x2 matrix [[a, b], [c, d]]?

Which conic section is described by the equation Ax^2 + By^2 = C?

What is the intersection point of the lines x - y = 3 and 2x + y = 1?

What is the equation of the line of reflection for the line y = 2x + 5?

What is the eigenvalue of a matrix?

What is the condition for three points to be collinear in the coordinate plane?

If two lines are parallel, what can be said about their slopes?

What is the equation of the sphere with center (h, k, l) and radius r?

What is the cross product of vectors A = <1, 2, 3> and B = <4, 5, 6>?

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