Today is our topic of discussion Coordinate geometry exercises 11-4 .
Coordinate geometry exercises 11-4
1. If A(-1,3) and B(2,5) then, AB’s
(i) length is √13 unit
(ii) slope is 2/3
(iii) equation is 2x – 3y = 11
Which of the followings is true?
1) i, ii
2) i, iii
3) ii, iii
4) i, ii and iii
2. In √(s(s – a)(s – b)(s – c)) s means
1) area of triangle
2) area of circle
3) half perimeter of triangle
4) half perimeter of circle.
3.
Area of the triangle is
1) 12 square unit
2) 15 square unit
3) 6 square unit
4) 60 square unit
4.
Slope of the line AB
1) 2
2) -2
3) 0
4) 6
5. Product of the slopes of x – 2y – 10 = 0 and 2x + y – 3 = 0 is
1) -2
2) 2
3) -3
4) -1
6. Equations and 5x – 10y + 20 = 0 indicate y = x/2 + 2
1) two different lines
2) the same line
3) that the two lines are parallel
4) that the two lines intersect each other
7. The intersecting point of y = x – 3 and y = – x + 3 is
1) (0,0)
2) (0,3)
3) (3,0)
4) (-3,3)
8. x = 1 y = 1 The coordinate of the point on which the two lines intersect x-axis is
1) (0,1)
2) (1,0)
3) (0,0)
4) (1,1)
9. 1, y = 1. The area of the region created by the two lines with the two axes is
1) square unit
2) 1 square unit
2 3) 2 square unit
4) 4 square unit
10. Find the equation of the straight line which passes through the point (2,-1) and whose slope is 2.
11. Find the equation of the straight line passing through each pair of points below:
1) A(1,5), B(2,4)
2) A(3,0), B(0,-3)
3) A(a,0), B(2a, 3a)
12. In each case given below, find the equation of the straight line
1) Slope is 3 and intersector of y is 5
2) Slope is 3 and intersector of y is 5
3) Slope is -3 and intersector of y is 5
4) Slope is -3 and intersector of y is -5
Draw these four straight lines on the same plane. [By these lines it will be understood in which quadrant the slope and the symbol indicating bisector will remain]
13. Find the points where each of the following straight lines intersects the x-axis and the y-axis. Also draw the lines.
1) y=3x-3
2) 3x-2y-40
3) 2y=5x+6
14. Find the equation of the straight line passing through the point (k, 0) and having slope k using k. Find k if the line passes through the point (5,6).
15. Find the equation of the straight line passing through the point (k², 2k) and having slope. If the line passes through the point (−2, 1), find the possible value of k.
16. A straight line with slope passes through the point A(-2,3). If the line passes through the point (3,k), what is the value of k?
17. A line with slope 3 passes through the point A(-1, 6) and intersects x-axis at the point B. Another line passing through the point A intersects x-axis at the point C(2, 0).
1) Find the equations of the lines AB and AC.
2) Find the area of ΔABC.
18. Show that the two lines y – 2x+4=0 and 3y = 6x + 10 do not intersect each other. By drawing the two lines, explain why the equation have no solution.
19. The three equations y = x + 5, y = −x + 5, and y = 2 indicate the three sides of a triangle. Draw the triangle and find the area.
20. Find the coordinate of the intersecting point of the two lines y = 3x+4 and 3x + y = 10. Draw the two lines and find the area of the triangle with x-axis.
21. Prove that the three lines 2yx = 2, y + x = 7 and y = 2×5 are concurrent, i.e., the lines pass through the same point.
22. y=x+3, y=x -3, y=x+3 and y = -x-3 indicate the four sides of a quadrilateral. Draw the quadrilateral and determine the area in three different methods.
23. A(-4, 13), B(8, 8), C(13, −4) and D(1, 1) are the vertices of a quadrilateral.
1) Determine the angle that line BD forms with x-axis.
2) Determine the characteristic of quadrilateral ABCD.
3) Determine the area of that portion of quadrilateral ABCD which forms a triangle with x-axis.
24. Four corner points of a quadrilateral are P(5, 2), Q(-3, 2), R(4, -1) and S(-2, -1)
1) Determine the equation of straight line PS.
2) Determine the length of the diagonal of the square that has the same area as that of quadrilateral PQSR.
3) Determine the area of that portion of quadrilateral PQSR which resides in the second quadrant.
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