Straight Lines Questions

MathematicsStraight Lines102 Questions Found

MathematicsVarious Forms of Equations of a LineJEE Advanced 2008

Consider the lines given by $L_{1} : x + 3 y - 5 = 0$ ; $L_{2} : 3 x - k y - 1 = 0$ ; $L_{3} : 5 x + 2 y - 12 = 0$ . Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the ORS.

List-I

(P)

L_{1}, L_{2}, L_{3}

are concurrent, if

(Q)

One of

L_{1}, L_{2}, L_{3}

is parallel to at least one of the other two, if

(R)

L_{1}, L_{2}, L_{3}

form a triangle, if

(S)

L_{1}, L_{2}, L_{3}

do not form a triangle, if

List-II

(1)

k = - 9

(2)

k = - \frac{6}{5}

(3)

k = \frac{5}{6}

(4)

k = 5

Answer:P → 4, P → 2, R → 3, S → NaN

MathematicsAngle Between Two LinesJEE Advanced 1989

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Let $A B C$ be a triangle with $A B = A C$ . If $D$ is the midpoint of $B C$ , $E$ is the foot of the perpendicular drawn from $D$ to $A C$ and $F$ the mid-point of $D E$ , prove that $A F$ is perpendicular to $B E$ .

MathematicsDistance and Section FormulasJEE Advanced 1997

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Let $S$ be a square of unit area. Consider any quadrilateral which has one vertex on each side of $S$ . If $a, b, c$ , and $d$ denote the lengths of the sides of the quadrilateral, prove that $2 \leq a^{2} + b^{2} + c^{2} + d^{2} \leq 4$ .

MathematicsCentroid, Incenter, Orthocenter, and CircumcenterJEE Advanced 1998

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Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.

MathematicsVarious Forms of Equations of a LineJEE Advanced 2000

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For points $P = (x_{1}, y_{1})$ and $Q = (x_{2}, y_{2})$ of the co-ordinate plane, a new distance $d (P, Q)$ is defined by $d (P, Q) = ∣ x_{1} - x_{2} ∣ + ∣ y_{1} - y_{2} ∣$ . Let $O = (0, 0)$ and $A = (3, 2)$ . Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from $O$ and $A$ consists of the union of a line segment of finite length and an infinite ray. Sketch this set in a labelled diagram.

MathematicsVarious Forms of Equations of a LineJEE Advanced 2002

View in:English Hindi

A straight line $L$ through the origin meets the lines $x + y = 1$ and $x + y = 3$ at $P$ and $Q$ respectively. Through $P$ and $Q$ two straight lines $L_{1}$ and $L_{2}$ are drawn, parallel to $2 x - y = 5$ and $3 x + y = 5$ respectively. Lines $L_{1}$ and $L_{2}$ intersect at $R$ . Show that the locus of $R$ , as $L$ varies, is a straight line.

MathematicsVarious Forms of Equations of a LineJEE Advanced 1978

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One side of a rectangle lies along the line $4 x + 7 y + 5 = 0$ . Two of its vertices are $(- 3, 1)$ and $(1, 1)$ . Find the equations of the other three sides.

Answer:4x + 7y - 11 = 0, 7x - 4y - 3 = 0, 7x - 4y + 25 = 0

MathematicsArea of TriangleJEE Advanced 1978

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The area of a triangle is 5. Two of its vertices are $A (2, 1)$ and $B (3, - 2)$ . The third vertex $C$ lies on $y = x + 3$ . Find $C$ .

Answer:(\frac{7}{2}, \frac{13}{2}) \text{ or } (-\frac{3}{2}, \frac{3}{2})

MathematicsDistance and Section FormulasJEE Advanced 1978

View in:English Hindi

A straight line segment of length $l$ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $1 : 2$ .

Answer:9x^2 + 36y^2 = 4l^2

MathematicsCentroid, Incenter, Orthocenter, and CircumcenterJEE Advanced 1979

View in:English Hindi

(a) Two vertices of a triangle are $(5, - 1)$ and $(- 2, 3)$ . If the orthocentre of the triangle is the origin, find the coordinates of the third point. (b) Find the equation of the line which bisects the obtuse angle between the lines $x - 2 y + 4 = 0$ and $4 x - 3 y + 2 = 0$ .

Answer:(a) (-4, -7), (b) (4-\sqrt{5})x + (2\sqrt{5}-3)y - (4\sqrt{5}-2) = 0

...11

List-I

List-II

Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } One side of a rectangle lies along the line 4x+7y+5=0. Two of its vertices are (−3,1) and (1,1). Find the equations of the other three sides.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of a triangle is 5. Two of its vertices are A(2,1) and B(3,−2). The third vertex C lies on y=x+3. Find C.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A straight line segment of length l moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio 1:2.

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } One side of a rectangle lies along the line 4x+7y+5=0. Two of its vertices are (−3,1) and (1,1). Find the equations of the other three sides.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of a triangle is 5. Two of its vertices are A(2,1) and B(3,−2). The third vertex C lies on y=x+3. Find C.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A straight line segment of length l moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio 1:2.

One side of a rectangle lies along the line $4 x + 7 y + 5 = 0$ . Two of its vertices are $(- 3, 1)$ and $(1, 1)$ . Find the equations of the other three sides.

The area of a triangle is 5. Two of its vertices are $A (2, 1)$ and $B (3, - 2)$ . The third vertex $C$ lies on $y = x + 3$ . Find $C$ .

A straight line segment of length $l$ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $1 : 2$ .

One side of a rectangle lies along the line $4 x + 7 y + 5 = 0$ . Two of its vertices are $(- 3, 1)$ and $(1, 1)$ . Find the equations of the other three sides.

The area of a triangle is 5. Two of its vertices are $A (2, 1)$ and $B (3, - 2)$ . The third vertex $C$ lies on $y = x + 3$ . Find $C$ .

A straight line segment of length $l$ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $1 : 2$ .