Coordinate Geometry Problems

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Questions and Answers

Reproduction is a principal feature of life.

False (B)

Metabolism involves only breaking down substances.

False (B)

Irritability refers to an organism's ability to respond to stimuli.

True (A)

The earliest atmosphere on Earth was rich in oxygen.

<p>False (B)</p> Signup and view all the answers

The first life forms used RNA but not DNA as their genetic material.

<p>True (A)</p> Signup and view all the answers

The chemical origin of life is referred to as biogenesis.

<p>False (B)</p> Signup and view all the answers

The Earth is estimated to be approximately 4.6 billion years old.

<p>True (A)</p> Signup and view all the answers

A 'naked gene' refers to a protein molecule not enclosed in a membrane.

<p>False (B)</p> Signup and view all the answers

Simple sugars like glucose can form from inorganic substances.

<p>True (A)</p> Signup and view all the answers

Proteins are made up of glycerol molecules.

<p>False (B)</p> Signup and view all the answers

The first cells were likely prokaryotic.

<p>True (A)</p> Signup and view all the answers

The early atmosphere contained abundant free oxygen produced by volcanoes.

<p>False (B)</p> Signup and view all the answers

ATP is the only source of energy for cells.

<p>False (B)</p> Signup and view all the answers

The earliest life forms were photosynthetic.

<p>False (B)</p> Signup and view all the answers

Coacervates are simple cells with a nucleus.

<p>False (B)</p> Signup and view all the answers

The biological evolution is also known as biogeny.

<p>True (A)</p> Signup and view all the answers

The primitive earth's atmosphere had high levels of $O_2$.

<p>False (B)</p> Signup and view all the answers

The age of the earth is 3.7 billion years.

<p>False (B)</p> Signup and view all the answers

The monomers of proteins are amino acids.

<p>True (A)</p> Signup and view all the answers

Metabolism refers to the process where organisms move from one place to another.

<p>False (B)</p> Signup and view all the answers

Flashcards

Reproduction

The ability to produce offspring, ensuring the continuation of species by creating new individual organisms.

Metabolism

The sum of all chemical processes that occur in an organism, including anabolism (building up) and catabolism (breaking down).

Irritability

The capacity of living organisms to respond to stimuli or changes in their environment.

Chemogony

The chemical origin of life from non-living matter.

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Naked gene

The process where the first cells were formed with only protein and RNA.

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Biogeny

The evolutionary process by which life originates from non-living matter.

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Study Notes

  • The problem sheet focuses on coordinate geometry.

Problems

  • Question 1 involves finding the equation of a line through two points, a perpendicular line, and their intersection. The points A, B, and C have coordinates (-2,1), (2,2), and (4,-3) respectively.
  • Question 2 asks for the equation of a line through a point perpendicular to a given line. The given line (L) has equation y = 5x - 3 and the point A has coordinates (3,4).
  • Question 3 involves finding equations of lines related to a triangle. The vertices of the triangle ABC have coordinates A(2,5), B(5,-1), and C(6,2).
  • Question 4 is about finding the intersection of two lines and a parallel line through a given point. The lines L1 and L2 have equations y = 3x + 5 and y = -2x + 1.
  • Question 5 deals with finding the perpendicular bisector of a line segment. The points A and B have coordinates (-3,5) and (5,-1).
  • Question 6 involves finding the value of k for parallel lines. The lines L1 and L2 have equations 4x + 6y = 3 and kx + 9y = 5.
  • Question 7 asks for the equation of a circle with a given center and radius. The circle has a center at (-1,4) and a radius of 5.
  • Question 8 requires finding the center and radius of a circle from its equation. The circle has the equation $x^2 + y^2 - 4x + 6y = 12$.
  • Question 9 involves finding the intersection of a circle and a line. The circle C has the equation $(x - 5)^2 + (y + 2)^2 = 20$
  • Question 10 is about finding the radius and tangent of a circle. The circle C has center (4,-1) and passes through the point P(7,3).
  • Question 11 asks for the point of contact of a tangent to a circle. The line y = x + 5 is a tangent to the circle with center (3,-2).

Solutions

  • 1a: x + 4y - 2 = 0
  • 1b: 4x - y - 19 = 0
  • 1c: (6, 5)
  • 2: y = -1/5 x + 23/5
  • 3a: 2x + y - 9 = 0
  • 3b: x - 2y - 2 = 0
  • 3c: y = -2/5 x
  • 4a: (-4/5, 11/5 )
  • 4b: y = 3x - 7
  • 5: 4x - 3y - 5 = 0
  • 6: k = 6
  • 7: $(x + 1)^2 + (y - 4)^2 = 25$
  • 8: center(2, -3), radius 5
  • 9a: center(5, -2), radius $2\sqrt{5}$
  • 9b: (3, -6) and (5, -10)
  • 10a: 5
  • 10b: 3x + 4y - 33 = 0
  • 11: (0, 5)

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