Coordinate Geometry Quiz

Grade 10 · Math · Quiz

Challenge your skills with coordinate geometry problems involving lines, circles, and distances.

Questions

1. What is the equation of the line through (2, 3) with slope −½?

   1. y = −½x + 4
   2. y = −½x + 2
   3. y = −½x + 3
   4. y = ½x + 4
   Show answer

   Answer: y = −½x + 4

   Using point-slope: y−3 = −½(x−2) → y = −½x + 1 + 3 = −½x + 4.

2. Find the radius of the circle x² + y² − 4x + 6y − 12 = 0.

   1. 5
   2. √12
   3. 4
   4. √25
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   Answer: 5

   Complete the square: (x−2)²+(y+3)²=4+9+12=25, so r=√25=5.

3. Which point lies on the circle (x−1)² + (y+2)² = 25?

   1. (4, 2)
   2. (1, −7)
   3. (−4, −2)
   4. (6, −2)
   Show answer

   Answer: (1, −7)

   Check: (1−1)²+(−7+2)²=0+25=25. ✓

4. What is the slope of the perpendicular bisector of the segment joining (0, 0) and (4, 2)?

   1. −2
   2. ½
   3. 2
   4. −½
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   Answer: −2

   Slope of PQ = (2−0)/(4−0) = ½. Perpendicular slope = −1/(½) = −2.

5. The line y = 2x + 5 is parallel to y = 2x − 3.

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   Answer: True

   Both lines have slope 2; parallel lines have equal slopes and different y-intercepts.

6. Points A(0,0), B(4,0), and C(4,3) form a triangle. What is the length of AC?

   1. 5
   2. 4
   3. 3
   4. 7
   Show answer

   Answer: 5

   AC = √[(4−0)²+(3−0)²] = √[16+9] = √25 = 5.

7. The midpoint of segment PQ is M(3, −1). If P = (1, 5), what are the coordinates of Q?

   1. (5, −7)
   2. (4, 2)
   3. (2, 4)
   4. (−1, 7)
   Show answer

   Answer: (5, −7)

   Midpoint formula: (1+Qx)/2=3 → Qx=5; (5+Qy)/2=−1 → Qy=−7.

8. The general equation of a circle can be converted to standard form by ______ the square.

   Show answer

   Answer: completing

   Completing the square on the x and y terms converts the general form to (x−h)²+(y−k)²=r².

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