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Mathematics Grade 10 Unit 7: Coordinate Geometry

22 national exam questions have come from this unit. It runs 40 pages; one careful study pass takes about 3.0 hours, and its difficulty is moderate among Mathematics units. Each section below lists the questions set from it, with the year, and opens the page that teaches it.

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7.1 Distance between two points · read p. 347
  • 2016 E.C., Q20 – The line $y = x$ is intersected by the horizontal line $y = a$ at point $P$ and $y = b$ at point $Q$ for $a ≠ b$. Which of the following gives the distance from $Q$ to $P$?
  • 2014 E.C., Q6 – Which of the following is true? A hyperbola is a locus of points in the plane so that:
7.2 Division of a line segment · read p. 351
  • 2017 E.C., Q35 – Consider the line segment $PQ$ with $P=(1,-1)$ and $Q=(4,2)$. Then which of the following point divides $PQ$ internally in the ratio of $2:1$?
  • 2016 E.C., Q18 – Which one of the following ordered pairs of numbers gives the coordinates of the point that divides a line segment with end points A(1, 1) and B(-6, 8) in the ratio of 3:4?
  • 2015 E.C., Q7 – In shown below, the medians and of are concurrent at point . If cm, cm and , then which one of the following is NOT true?
  • 2014 E.C., Q43 – What are the coordinates of a point that divides the line segment with endpoints P(0, 1) and Q(5, 6) in the ratio 2:3 from P?
7.3 Equation of a line · read p. 356
  • 2018 E.C., Q17 – A line is passing through the points $(-2, 5)$ and $(3, -5)$. What is the gradient of the line?
  • 2018 E.C., Q11 – Which one of the following equations represents a line that passes through the points $(2, -1)$ and $(-3, 4)$?
  • 2017 E.C., Q26 – What is the equation of a line that passes through $(-2,5)$ and has a slope $\frac{1}{2}$?
  • 2015 E.C., Q26 – Consider the lines and . Then the angle between and is
  • 2015 E.C., Q10 – The slope of the line that makes an angle of 135° with the positive x-axis is equal to
7.4 Slopes of parallel and perpendicular lines · read p. 365
  • 2018 E.C., Q2 – Consider the quadrilateral ABCD where $A=(0,0)$, $B=(-1,1)$, $C=(0,2)$ and $D=(2,2)$. Which one of the following is true?
  • 2016 E.C., Q34 – Which of the following pairs of lines with the given equations are parallel?
7.5 Equation of a Circle · read p. 370
  • 2016 E.C., Q11 – Which one of the following conic section is defined by "the set of points in a plane such that the sum of the distances from two given points is constant"?
  • 2015 E.C., Q13 – If the foci of a hyperbola are $(-2, 4)$ and $(8, 4)$ and the transverse axis is 8 cm long, which one of the following is the standard form of equation of the hyperbola?
  • 2014 E.C., Q1 – What is the locus all points in the plane in which the sum of the distances from two fixed points is constant?
  • 2014 E.C., Q4 – Which one of the following is the equation of a circle with center (2, -1) and radius 3 units?
  • 2013 E.C., Q9 – The equation of a circle is given by $(x-3)^2+(y+2)^2=9$. What are the center and the radius of the circle respectively?
  • 2013 E.C., Q2 – Which one of the following is the standard form of the equation of the circle centered at $(2, -3)$ and radius 5?
7.6 Applications · read p. 375
  • 2014 E.C., Q58 – What is the point of intersection of the medians of ΔABC whose vertices are given by A(0, 0), B(6, 0) and C(0, 1)?