TS EAPCET (Engineering) Straight Lines — practice questions
80 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Straight Lines in the app →Between which limits does the inclination of any line lie?What is the inclination of a line parallel to the y-axis?If a line has inclination θ, its slope is defined asA line makes an inclination of 45° with the positive x-axis. Its slope isFind the slope of the line through (3, –2) and (–1, 4).Two non-vertical lines are parallel exactly when their slopes areThe product of the slopes of two perpendicular non-vertical lines isA line of slope 2/3 is perpendicular to a line of slopeThe line through (–2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (x, 24). Find x.Three points on one straight line form a triangle whose area isFind the area of the triangle with vertices (0, 0), (4, 0) and (0, 6).Which French mathematician published La Géométrie in 1637, introducing the equation of a curve?The study of geometry using algebra is calledA horizontal line lies 5 units above the x-axis. Its equation isThe line through (–2, 3) parallel to the x-axis has equationThe point-slope form of a line through (x0, y0) with slope m isFind the line through (–2, 3) with slope –4.Deriving the two-point form uses the fact that three points on the line areThe line through (1, –1) and (3, 5) has y-interceptThe slope-intercept form of a line isWhat is the y-intercept of the line y = 3x – 7?A line with y-intercept c cuts the y-axis at the pointFind the line with slope 2 and y-intercept 3.The intercept form of a line with x-intercept a and y-intercept b isA line has x-intercept 4 and y-intercept 6. Its equation isAx + By + C = 0 is a general linear equation providedThe slope of the line Ax + By + C = 0 (B ≠ 0) isThe distance of a point from a line is the length of theFind the distance of (3, –5) from the line 3x – 4y – 26 = 0.The distance between Ax + By + C1 = 0 and Ax + By + C2 = 0 isThe acute angle θ between lines of slopes m1 and m2 satisfies tan θ =Find the acute angle between the line y = x and the x-axis.Two lines have slopes 1/2 and 1/3. The tangent of the acute angle between them isLines with slopes 2 and –1/2 meet at an angle ofIf the acute angle between two lines is 30°, the obtuse angle between them isIf (m2 – m1)/(1 + m1m2) is positive, the angle θ between the lines isTwo lines meet at 45° and one has slope 0. The other slope can beFind the slope of the line from the origin to the mid-point of the segment joining (0, –4) and (8, 0).A line makes 30° with the positive y-axis, measured anticlockwise. Its slope isThe line joining (3, –1) and (4, –2) makes what angle with the positive x-axis?A line through (2, 3) cuts equal intercepts on both axes. Its equation isIn triangle PQR with P(2, 1), Q(–2, 3), R(4, 5), the median through R isThe points (3, 0), (–2, –2) and (8, 2) are collinear since the slopes of the segments from (3, 0) to the otherL (cm) is linear in C: 124.942 at 20 and 125.134 at 110. L rises per degree byLinear demand: 980 L at Rs 14 and 1220 L at Rs 16. Sales at Rs 17 areThe point on the x-axis equidistant from (7, 6) and (3, 4) isAn equilateral triangle has a base of length 4 on the y-axis centred at the origin. A third vertex isA line perpendicular to the segment from the origin to (–2, 9) passes through (–2, 9). Its equation isA segment between the axes has mid-point P(a, b). Its x-intercept isR(h, k) divides the segment from (p, 0) to (0, q) in the ratio 1:2. Then p equalsThe line through (–2, 3) parallel to 3x – 4y + 2 = 0 isA line through (1, 2) and (3, 8) is parallel to every line of slopeThe lines 2x – y + 1 = 0 and x + 2y – 3 = 0 areWhat is the slope of a line whose inclination is 60 degrees?The origin is shifted to O'(2, 3). What are the new co-ordinates of (5, 7)?The inclination θ of a line, measured anticlockwise from the positive x-axis, lies in which interval?For a vertical line, the slope isA line has inclination 135°. What is its slope?What are the slopes of the x-axis and the y-axis respectively?A line joins the points (−1, 4) and (3, −4). What is its slope?The slope of a line inclined at 60° to the positive x-axis isA line joining the origin to the point (1, √3) has inclinationThe points (3, 2) and (3, 7) lie on a line whose slope isTwo lines have slopes 3k − 1 and 5. For what value of k are they parallel?Two lines meet at 45°, and one has slope 1/2. Which could be the slope of the other?The lines y = x and y = √3 x meet at an acute angle ofWhich line passes through (−2, 3) and is parallel to the y-axis?Which equation represents the line through the points (1, −1) and (3, 5)?A line passes through (−1, 2) and (3, −2). Its equation isA line has slope 2 and cuts the y-axis at −5. Its equation isThe line through the origin inclined at 45° to the x-axis isA line makes intercepts −3 and 2 on the x- and y-axes. Its equation isWhich line cuts off intercepts 4 on the x-axis and 5 on the y-axis?The line 3x + 4y = 12 and the two coordinate axes enclose a triangle of areaIn the general linear equation Ax + By + C = 0, what must hold for A and B?What is the perpendicular distance of the point (2, 1) from the line 3x − 4y + 5 = 0?Find the distance between the parallel lines y = 2x + 3 and y = 2x − 2.A line is perpendicular to 2x − 3y + 4 = 0. What is its slope?The points (1, 2), (3, 6) and (k, 10) are collinear. Find k.The lines 3x + 2y − 5 = 0 and kx + 4y + 1 = 0 are parallel. Find k.