Coordinate Geometry

The initiator of analytical geometry is —

The coordinate system initiated by Descartes is called —

The portion of geometry studying algebraic expressions of points and lines is —

Two mutually perpendicular straight lines $XOX'$ and $YOY'$ intersect at the —

The horizontal line $XOX'$ is called the —

The perpendicular distance of a point $P$ from the y-axis is called its —

The perpendicular distance of a point $P$ from the x-axis is called its —

In $P(x, y)$, $x$ is the abscissa and $y$ is the —

$(x, y)$ is called an —

If $x \neq y$, the points $(x, y)$ and $(y, x)$ are —

The ordinate of any point lying on the x-axis is —

The abscissa of any point lying on the y-axis is —

The number of quadrants of the Cartesian plane is —

Quadrants are numbered from $XOY$ moving in —

The point $(-3, -5)$ lies in the —

A point with sign $(+, -)$ lies in the —

The point $(4, -2)$ lies in the —

Consider the following statements about Cartesian coordinates:

The distance between $P(x_1, y_1)$ and $Q(x_2, y_2)$ is —

The distance of $P(x, y)$ from the origin is —

For two points $P$ and $Q$, the distances $PQ$ and $QP$ are —

The distance between two points is always —

The distance between $P(1, 1)$ and $Q(2, 2)$ is —

The distance between $O(0, 0)$ and $P(3, 0)$ is —

The distance between $P(3, 0)$ and $Q(0, 3)$ is —

The triangle formed by $O(0,0)$, $P(3,0)$, $Q(0,3)$ is —

The perimeter of the triangle with vertices $A(2,0)$, $B(7,0)$, $C(3,4)$ is —

The points $(0, -1)$, $(-2, 3)$, $(6, 7)$, $(8, 3)$ are vertices of a —

The points $(-3, -3)$, $(0, 0)$, $(3, 3)$ —

The distance between $(2, 3)$ and $(4, 6)$ is —

The distance between $(-3, 7)$ and $(-7, 3)$ is —

The distance between $(a, b)$ and $(b, a)$ is —

The distance between $(0, 0)$ and $(\sin\theta, \cos\theta)$ is —

The triangle with vertices $A(2,-4)$, $B(-4,4)$, $C(3,3)$ is —

The triangle with vertices $A(2,5)$, $B(-1,1)$, $C(2,1)$ is —

The points $A(1,2)$, $B(-3,5)$, $C(5,-1)$ —

The perimeter of the equilateral triangle with vertices $A(2,2)$, $B(-2,-2)$, $C(-2\sqrt{3},2\sqrt{3})$ up to three decimal places is approximately —

Among $A(10,5)$, $B(7,6)$, $C(-3,5)$, the point nearest to $P(3,-2)$ is —

Among $A(10,5)$, $B(7,6)$, $C(-3,5)$, the point farthest from $P(3,-2)$ is —

If the distance from $P(x, y)$ to the y-axis equals the distance from $P(x, y)$ to $Q(3, 2)$, then the relation is —

Heron's formula for the area of a triangle is —

In Heron's formula, $s$ denotes —

If sides of a triangle are 3, 4, 5 units, its area is —

The area of $\triangle ABC$ with $A(2,5)$, $B(-1,1)$, $C(2,1)$ is —

The area of $\triangle ABC$ with $A(2,-4)$, $B(-4,4)$, $C(3,3)$ is —

The triangle with vertices $A(2,-4)$, $B(-4,4)$, $C(3,3)$ is —

The area of the triangle with vertices $A(-2,0)$, $B(5,0)$, $C(1,4)$ is —

The triangle $A(-2,0)$, $B(5,0)$, $C(1,4)$ is —

The quadrilateral with vertices $A(1,0)$, $B(0,1)$, $C(-1,0)$, $D(0,-1)$ is a —

The area of the quadrilateral $A(1,0)$, $B(0,1)$, $C(-1,0)$, $D(0,-1)$ is —

The area of the irregular quadrilateral with vertices $A(-1,1)$, $B(2,-1)$, $C(3,3)$, $D(1,6)$ is approximately —

The quadrilateral with vertices $A(2,-3)$, $B(3,0)$, $C(0,1)$, $D(-1,-2)$ is a —

Each diagonal of the square $A(2,-3)$, $B(3,0)$, $C(0,1)$, $D(-1,-2)$ has length —

The area of the square with vertices $A(2,-3)$, $B(3,0)$, $C(0,1)$, $D(-1,-2)$ is —

In the coordinate (determinant) area formula, vertices must be taken in —

The area of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ in anti-clockwise order is —

Method 2 (using coordinates) is most useful when —

The area of $\triangle ABC$ with $A(2,3)$, $B(5,6)$, $C(-1,4)$ is —

The vertices of $\triangle ABC$ are $A(1,3)$, $B(5,1)$, $C(3,r)$ and area is 4 sq unit. The possible values of $r$ are —

The area of the quadrilateral $A(1,4)$, $B(-4,3)$, $C(1,-2)$, $D(4,0)$ is —

To compute the area of a quadrilateral by Method 2, divide it into —

The area of a pentagon by Method 2 is the sum of —

The perimeter of $\triangle ABC$ with $A(-2,0)$, $B(5,0)$, $C(1,4)$ is —

The area of $\triangle ABC$ with $A(5,2)$, $B(1,6)$, $C(-2,-3)$ is —

The points $A(1,1)$, $B(4,4)$, $C(4,8)$, $D(1,5)$ form a —

If $A(-2,1)$, $B(10,6)$, $C(a,-6)$ and $AB = BC$, the possible values of $a$ are —

The slope (gradient) of a straight line equals —

If a line makes angle $\theta$ with the positive x-axis, then its slope $m$ equals —

The slope of a line parallel to the x-axis is —

The slope of a line parallel to the y-axis is —

If the slope of a line is positive, the angle it makes with the positive x-axis is —

If the slope of a line is negative, the angle it makes with the positive x-axis is —

The slope of the line through $A(2,3)$ and $B(3,6)$ is —

The slope of the line through $A'(2,1)$ and $B'(-1,4)$ is —

The slope of the line through $A(2,2)$ and $C(2,7)$ is —

The slope of the line through $A(-3, 2)$ and $B(3, -2)$ is —

If $A(1,-1)$, $B(2,2)$, $C(4,t)$ are collinear, then $t$ equals —

If $A(t, 3t)$, $B(t^2, 2t)$, $C(t-2, t)$, $D(1, 1)$ and $AB \parallel CD$, the admissible values of $t$ are —

The slope of the line through $A(5,-2)$ and $B(2,1)$ is —

The slope of the line through $A(3,5)$ and $B(-1,-1)$ is —

The slope of the line through $A(t, t)$ and $B(t^2, t)$ (with $t \neq t^2$) is —

The slope of the line through $A(t, t+1)$ and $B(3t, 5t+1)$ is —

The points $A(0, -3)$, $B(4, -2)$, $C(16, 1)$ are —

If $A(1, -1)$, $B(t, 2)$, $C(t^2, t+3)$ are collinear, the admissible value of $t$ is —

If the slope of the line through $A(3, 3p)$ and $B(4, p^2+1)$ is $-1$, then $p$ equals —

The equation of a straight line through $(x_1, y_1)$ with slope $m$ is —

The slope-intercept form of a straight line is —

In $y = mx + c$, the constant $c$ represents the —

The equation of the x-axis is —

The equation of the y-axis is —

The equation of a line parallel to the y-axis through the point $(a, 0)$ is —

The equation of a line parallel to the x-axis through the point $(0, b)$ is —

If the line $y = mx + c$ passes through the origin, then —

The equation of the straight line through $A(3, 4)$ and $B(6, 7)$ is —

The equation of the straight line through $(-2, -3)$ with slope 3 is —

The line $y = 3x + 3$ passes through $P(t, 4)$. Then $t$ equals —

The line $y = 3x + 3$ intersects the x-axis at —

The line $y = 3x + 3$ intersects the y-axis at —

The slope and y-intercept of $y - 2x + 3 = 0$ are —

The equation of the line through $A(-1, 3)$ and $B(5, 15)$ is —

The line $y = 2x + 5$ intersects the x-axis at —

If the line $y = 2x + 5$ meets the x-axis at $P$ and the y-axis at $Q$, the length $PQ$ is —

The equation of the line through $A(1, 5)$ and $B(2, 4)$ is —

The equation of the line through $A(3, 0)$ and $B(0, -3)$ is —

The equation of the line through $A(a, 0)$ and $B(2a, 3a)$ is —

The equation of the line with slope 3 and y-intercept 5 is —

The line $y = 3x - 3$ meets the x-axis and y-axis respectively at —

A line through $(4, 0)$ with slope $k$ passes through $(5, 6)$. Then $k$ equals —

A line with slope $\frac{1}{3}$ through $A(-2, 3)$ passes through $(3, k)$. Then $k$ equals —