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Coordinate Geometry: CBSE Class 10 Mathematics practice questions

Practise 50 questions on Coordinate Geometry, free, with an explanation for each answer.

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Sample questions

Town BB is 2424 km east and 77 km north of town AA. Without measuring, what is the straight-line distance ABAB?

Two towns with a right triangle formed by the east and north distances
  1. 31 km
  2. 17 km
  3. 625 km
  4. 25 km
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D. 25 km

The east and north distances are the two legs of a right triangle, so AB=242+72=625=25AB=\sqrt{24^2+7^2}=\sqrt{625}=25 km. Adding the legs (31) ignores the shortcut across; subtracting (17) is meaningless; 625 forgets the square root.

Find the distance between P(5,3)P(5, 3) and Q(−4,−9)Q(-4, -9).

The points P and Q in different quadrants joined by a segment
  1. 1515
  2. 37\sqrt{37}
  3. 2121
  4. 225225
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A. 1515

PQ=(−4−5)2+(−9−3)2=81+144=225=15PQ=\sqrt{(-4-5)^2+(-9-3)^2}=\sqrt{81+144}=\sqrt{225}=15. Adding the coordinates instead of subtracting gives 37\sqrt{37}; adding the differences 9 and 12 gives 21; forgetting the root gives 225.

A point P(x,y)P(x, y) is equidistant from (at the same distance from) A(6,1)A(6, 1) and B(2,5)B(2, 5). Which relation between xx and yy is true?

Point P joined by equal dashed lines to A and B
  1. x+y=7x + y = 7
  2. x−y=1x - y = 1
  3. x−y=−1x - y = -1
  4. x−y=5x - y = 5
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B. x−y=1x - y = 1

(x−6)2+(y−1)2=(x−2)2+(y−5)2⇒−12x−2y+37=−4x−10y+29⇒−8x+8y=−8(x-6)^2+(y-1)^2=(x-2)^2+(y-5)^2 \Rightarrow -12x-2y+37=-4x-10y+29 \Rightarrow -8x+8y=-8, i.e. x−y=1x-y=1. The equation x+y=7x+y=7 is the line through AA and BB, not their perpendicular bisector; x−y=−1x-y=-1 is a sign slip; x−y=5x-y=5 is the line through AA parallel to the bisector.

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