Chapter 4 | Introduction to Analytic Geometry | Entry Test Preparation

Welcome to your Chapter 4(Introduction to Analytical Geometry)

Name

Class

Which pair of line are $\perp$ to each other?

$4x+3y-7=0,\,2x+7y+4=0$

$2x+2y=1,\,3x+3y=1$

$x-2y-6=0,\,2x+y-5=0$

$7x-3y=17,\,5x+2y=9$

The area of the triangle formed by the lines $7x-y-10=0$, $10x+y-41=0$ and $3x+2y+3=0$ is;

17 square units

34 square units

68 square units

7.5 square units

Distance of the point $(-7,13)$ from the line $2x+y+13=0$ is;

$56$

$\frac{6}{\sqrt{109}}$

$\frac{12}{\sqrt{5}}$

$67$

If a line passes through points $(4,3)$ and $(2,\lambda)$ will be shifted into;

$(0,-2)$

$(2,2)$

$(-2,1)$

$(-2,-2)$

Slope of line parallel to $x-axis$ is;

$2$

$\infty$

$0$

$1$

$y=-\frac{17}{9}x+\frac{37}{9}$ is _______ form equation $9y+17x-37=0$.

Normal

point - Slope

Interaction

Slope-intercept

Slope of a line parallel to y-axis is;

$0$

$-1$

undefined

$1$

Equation of hypotenuse $\overline{AB}$ of length $\sqrt{2}$ in isosceles $\triangle \, OAB$ is

$x+\sqrt{2y}=1$

$\sqrt{2}x+y=1$

$x+y=1$

$x+y=\sqrt{2}$

The slope formula is given by;

$m=\frac{y_2+y_1}{x_2-x_1}$

$m=\frac{y_2+y_1}{x_2+x_1}$

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{x_2+x_1}{y_2+y_1}$

The points $(4, -2), (-2, 4)$ and $(5, 5)$ are the vertices of a triangle. Then the coordinates of the in centre of the triangle are _______ ?

$(\frac{3}{2}, \frac{3}{2})$

$(3, -3)$

$(\frac{7}{2}, \frac{2}{7})$

$(\frac{5}{2}, \frac{5}{2})$

The distance between the parallel lines $4x+3y-2=0$ and $4x+3y+8=0$ is;

$12$

$2$

$\frac{13}{2}$

$\frac{59}{3}$

Which is the intercept form of the equation $px+qy+r=0$?

$x\cos{\alpha}+y\sin{\alpha}=1$

$\frac{x}{p}+\frac{y}{q}=1$

None

$y=mx+r$

Any equation of first degree in x and y represents a;

quadratic equation

line

Triangle

rectangle

The average entry test score of engineering candidates was 592 in the year 1998, while the score was 564 in 2002. assuming that the relationship between time and score is linear, then the average score in the year 2006 will be;

$350$

$536$

$450$

$650$

The measure of the angle from the first line to the second line whose slopes are $0$ and $3$, is;

$\tan^{-1}(3)$

$2\tan^{-1}(3)$

$\frac{1}{2}\tan^{-1}(7)$

$\tan^{-1}(\frac{1}{3})$

$A(0,b), B(0,0)$ and $C(a,0)$ are vertices of a triangle. Its median AD and mutually perpendicular if;

$b=-\sqrt{2}a$

$a=\frac{b}{\sqrt{2}}$

$a=\pm\sqrt{2}b$

$a=\sqrt{2}b$

The equation of the straight line through the point of intersection of $16x-10y-33=0, 12x+14y+29=0$ and the intersection of $x-y+4=0, x-7y+2=0$ is;

$13x+29y+66=0$

$13x+29y-66=0$

$13x-29y+66=0$

$13x-29y-66=0$

The points $(5,-2), (1,2), (-2,5)$ are;

vertices of rectangle

Collinear

Vertices of $\triangle$

all

If $\overline{AB}:\overline{BC}=2:3$ then point C divides the line segment $AB$ externally in ratio

$2:3$

$1:3$

$3:2$

$3:5$

Point of intersection of pair of lines $7x+2y=6$ and $3x+y=0$;

$(17,9)$

$(3,\,-\frac{1}{2})$

$(-6,-1)$

$(6, -18)$

Find $'b'$ if the line through $(3,4)$ and $(-1,b)$ is parallel to the line through $(2,3)$ and $(-4,1)$.

$-\frac{11}{15}$

$20$

$\frac{20}{7}$

$17$

Directed between the lines $4x+3y=11$ and $ 8x+6y=15$ is _________.

$\frac{15}{10}$

$\frac{7}{2}$

$\frac{7}{10}$

$4$

Centroid of a triangle with vertices $A(2, 3), B(-1, 6)$ and $C(7, 5)$ is

$(\frac{2}{5}, \frac{7}{3})$

$(\frac{1}{3}, \frac{2}{7})$

$(\frac{7}{3}, \frac{11}{3})$

$(\frac{8}{3}, \frac{14}{3})$

If the sum of the distances of a point from two $\perp$ lines is 1 then the locus is ___-

straight line

two intersecting straight lines

circle

square

The measure of the angle $\theta$ from the line $p_1x+q_1x+r_1=0$ to the line $p_2x+q_2y+r_2=0$, is given by $\tan{\theta}$=______;

$\frac{p_1q_2+q_2q_1}{p_1q_2-p_2q_1}$

$\frac{p_1q_2+p_2q_1}{p_1p_2-p_1q_2}$

None of these

$\frac{p_1q_1+p_2q_2}{p_1q_2-p_2q_1}$

Equation of line having slope 3 making x-intercept 5 is

$-3x+y+15=0$

$x+\frac{1}{3}y-5=0$

$y=3x+5$

$3x-y+5=0$

The equation of the line through the point $(-2,1)$ and the point of interaction of the lines $4x+3y-1=0$ and $2x-6y+5=0$ is;

$x-13y+19=0$

$23x-43y+27=0$

$8x+51y-35=0$

$18x+29y-21=0$

The points $(7, 9), (3, -7)$ and $(-3, 3)$ are the vertices of

An isosceles $\Delta$

A right angled $\Delta$

A right angled isosceles $\Delta$

An equilateral $\Delta$

The equation of line through $(-3, 5)$ and $\perp$ to line $x+2y+3=0$ is;

$y+2x+7=0$

$3x+7y+20=0$

$2x-y+11=0$

$4y+13x=19$

The inclination of any line parallel to y-axis is

$\frac{\pi}{2}$

$\frac{3\pi}{2}$

$\frac{\pi}{4}$

$0$

Which point is above the line $\frac{4}{3}x+y=1?$

$(-4,-1)$

$(3,1)$

$(-3,-1)$

$(-3,1)$

Joint equation of lines through the origin and perpendicular to the lines $x^2+xy-6y^2=0$

None of these

$6x^2+xy-y^2=0$

$-6x^2+x+y^2=0$

$-6x^2-xy-y^2=0$

The xy-coordinates are rotated about origin at an angle $180^o$ , then the coordinates of the point $P(4,-1)$ are;

$(-4,1)$

$(-4,-1)$

$(1,4)$

$(-1,4)$

The equation of line through $(x_2, y_2)$ perpendicular to the line $px+qy+r=0$ is;

$qx_2-py_2-qx+py=0$

$px+qy+px_2+qy_2=0$

$px_2+qy_2=0$

$px_2+qy_2+3px-3qy=0$

If the gradient of the line passing through $A(3,2)$ is $\frac{3}{4}$, the points on the at a distance 5 units from A are;

$(-7,5), (-1,-1)$

$(7,5), (-1,-1)$

$(-7,-5), (1,1)$

$(1,1), (5,-5)$

Two lines are parallel if and only if they have same;

quadrants

slope

Distance

vertices

The equation of the line through the points $(2,4)$ and $(7,1)$ is;

$2\sqrt{5}y+16x-13$

$5y+3x=0$

$5y+3x-26=0$

$9x+2y+17$

The vertices of a $\triangle \, ABC$ are $(2,2), (-4,-4)$ and $(5,-8)$ respectively, the length of the median through C is_________

$\sqrt{65}$

$\sqrt{113}$

$\sqrt{85}$

$\sqrt{117}$

The line segment joining by the points $(-3,-4)$ and $(1,-2)$ is divide by y-axis in the ratio

$1:3$

$2:3$

$3:2$

$3:1$

The matrix form of the system of linear equations; $3x+4y-7=0$ , $2x-5y+8=0$ , $x+y-3=0$

$\begin{bmatrix} 3 & 4 & -7 \\ 2 & -5 & 8 \\ 1 & 1 & -3 \end{bmatrix}$$\begin{bmatrix} x \\ y \\ 1 \end{bmatrix}$$=\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$

$\begin{bmatrix} 3x+4y-7=0 \\ 2x-5y+8=0 \\ x+y-3=0 \end{bmatrix}$

$\begin{bmatrix} 3 & 4 & -7 \\ 2 & -5 & 8 \\ 1 & 1 & -3 \end{bmatrix}$$\begin{bmatrix} x \\ y \\ z \end{bmatrix}$$=\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$

None of these

The inclination of the x-axis is;

$180^{o}$

$90^{o}$

$150^{o}$

$0^{o}$

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