Introduction :
Geometry is a branch of mathematics, which deals with lines, curves, solids, surfaces and points in space. In geometry, a point has a position only and is represented by a dot. A point has no length, width, or thickness. A line has length but no thickness or width. The position of a line with end points are called line segment.
How to solve Geometry Problems:
Geometry Problem 1:
Solve the equation of the straight line parallel to 6x + 4y = 12 and which passes through the point (3, − 3).
Solution:
The straight line parallel to 6x + 4y − 12 = 0 is of the form
6x + 4y + k = 0 … (1)
the point (3, − 3) satisfies the equation (1)
Hence 18 − 12 + k = 0 i.e. k = -6
3x + 2y - 6 = 0 is the equation of the required straight line.
Geometry Problem 2:
Solve the equation of the straight-line perpendicular to the straight line 3x + 4y + 28 = 0 and passing through the point (− 1, 4).
Solution:
The equation of any straight- line perpendicular to 3x + 4y + 28 = 0 is of the form4x − 3y + k = 0
the point (− 1, 4) lies on the straight line 4x − 3y + k = 0
− 4 − 12 + k = 0 ⇒ k = 16
the equation of the required straight line is 4x − 3y + 16 = 0
Geometry problem 3:
The lengths of two sides of right triangle are 7 cm and 24cm. Find its hypotenuses.
Solution:
AC = 7 cm
BC = 24 cm
AB = ?
AB^2 = 7^2 + 24^2
= 49 + 576
AB^2 = 625
AB = √625 = 25
Thus, the hypotenuses are 25 cms in length.
Geometry Problems to practice:
1) Solve the equation of straight line passing through the points (1, 2) and (3, − 4).
Ans: 3x+y = 5
2) Solve the distance between the parallel lines 2x + 3y − 6=0 and 2x + 3y + 7 = 0.
Ans: √13 units
3) Find the point of intersection of the straight lines 5x + 4y − 13 = 0 and 3x + y − 5 = 0.
Ans: The point of intersection is (1, 2)
4) Solve the equation of the curve formed by the set of all those points the sum of whose distances from the points A (4, 0, 0) and B (-4, 0, 0) is 10 units.
Ans: 9x^2+25y^2+25z^2-225=0.
Geometry is a branch of mathematics, which deals with lines, curves, solids, surfaces and points in space. In geometry, a point has a position only and is represented by a dot. A point has no length, width, or thickness. A line has length but no thickness or width. The position of a line with end points are called line segment.
How to solve Geometry Problems:
Geometry Problem 1:
Solve the equation of the straight line parallel to 6x + 4y = 12 and which passes through the point (3, − 3).
Solution:
The straight line parallel to 6x + 4y − 12 = 0 is of the form
6x + 4y + k = 0 … (1)
the point (3, − 3) satisfies the equation (1)
Hence 18 − 12 + k = 0 i.e. k = -6
3x + 2y - 6 = 0 is the equation of the required straight line.
Geometry Problem 2:
Solve the equation of the straight-line perpendicular to the straight line 3x + 4y + 28 = 0 and passing through the point (− 1, 4).
Solution:
The equation of any straight- line perpendicular to 3x + 4y + 28 = 0 is of the form4x − 3y + k = 0
the point (− 1, 4) lies on the straight line 4x − 3y + k = 0
− 4 − 12 + k = 0 ⇒ k = 16
the equation of the required straight line is 4x − 3y + 16 = 0
Geometry problem 3:
The lengths of two sides of right triangle are 7 cm and 24cm. Find its hypotenuses.
Solution:
AC = 7 cm
BC = 24 cm
AB = ?
AB^2 = 7^2 + 24^2
= 49 + 576
AB^2 = 625
AB = √625 = 25
Thus, the hypotenuses are 25 cms in length.
Geometry Problems to practice:
1) Solve the equation of straight line passing through the points (1, 2) and (3, − 4).
Ans: 3x+y = 5
2) Solve the distance between the parallel lines 2x + 3y − 6=0 and 2x + 3y + 7 = 0.
Ans: √13 units
3) Find the point of intersection of the straight lines 5x + 4y − 13 = 0 and 3x + y − 5 = 0.
Ans: The point of intersection is (1, 2)
4) Solve the equation of the curve formed by the set of all those points the sum of whose distances from the points A (4, 0, 0) and B (-4, 0, 0) is 10 units.
Ans: 9x^2+25y^2+25z^2-225=0.
No comments:
Post a Comment