Line - math word problems - page 22 of 30
Number of problems found: 600
- Three points 2
The three points are A(3, 8), B(6, 2), and C(10, 2). Point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D. - Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C? - Line segment
The 4 cm long line segment is enlarged in the ratio of 5/2. How many centimeters will the new line segment be long? - Coordinate axes
Find the triangle area given by line -7x+7y+63=0 and coordinate axes x and y. - Trapezoid - intersection of diagonals
In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate the trapezoid area. - Pupils' exercise
On part of the school playground there are embedded markers. Neighbouring markers are 60 cm apart from each other and form a square grid. The teacher said: line up on the markers in rows of three. Change places into rows of four. Stand in rows of six. We - Three Groups Work Shifts
A group of fitters installed the cable line in 9 changes, and the second group completed the same task in 1/3 less time. How many shifts would the third group do the same work if, with all three groups working together, the assembly took 2 shifts? - Number Between Two Values
Which number is also on the number axis from numbers 299 and 1051? - Map Scale Distance Calculation
The air distance from the hotel to the castle is 4.4 km. What is the map's scale on which this distance is shown by a line 4 cm long? - Sphere equation
Find the equation of a sphere whose centre lies on the line defined by 3x + 2z = 0 and 4x − 5y = 0, and which passes through the points (0, −2, −4) and (2, −1, 1). - Equation of circle 2
Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x. - Z7-I-5 MO 2017
Prokop constructed a triangle ABC whose interior angle at vertex A was greater than 60° and whose interior angle at vertex B was less than 60°. Juraj drew, in the half-plane determined by line AB and point C, a point D such that triangle ABD was equilater - Cyclist speed
Two cyclists set out simultaneously toward each other from opposite ends of a 28 km route. Each rode at a constant speed, with the faster cyclist reaching the finish line 35 minutes earlier. The cyclists passed each other after 1 hour of riding. At what s - 3N on the number axis
The line represents the number axis, and the marked points correspond to the numbers a, - a, and a + 1, but in no particular order. Construct the points that correspond to the numbers 0 and 1. Discuss all the possibilities. - Number line arrangement
On a number line, consider the points corresponding to the values a, 2a, and 3a + 1 arranged in all possible orders. For each arrangement, decide whether it is possible. If yes, give a specific example; if not, explain why. - Triangle line
The picture shows an isosceles triangle VLK with a center of gravity of T. The base VL measures 16 cm, and the line KK1 measures 18 cm. How long is the VV1 line? - Tangent
What distance are the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Grid Coloring Puzzle
Let's have a 4x6 grid, i.e., with 5x7 grid points. Can each grid point be colored white or blue so that each point has an even number of white neighbors? At the same time, those points that are connected by one line of the grid are considered to be neighb - Number line arrangement
On a number line, arrange the points corresponding to the values a, 2a, and 3a + 1 in all possible orders. For each arrangement, decide whether it is possible. If yes, give a specific example; if not, explain why. - Circumscribed by triangle
Inside the rectangle ABCD, the points E and F lie so that the line segments EA, ED, EF, FB, and FC are congruent. Side AB is 22 cm long, and the circle circumscribed by triangle AFD has a radius of 10 cm. Determine the length of side BC.
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