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Interactive multiple-choice quiz: Distance on the Coordinate Plane
يتناول هذا الملف مراجعة شاملة لدرس المسافة في المستوى الإحداثي.
🏆 انضم إلى التحدي واحصل على ترتيبك
اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
ابدأ السباق ✨
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
🚩 Report
Which of the following represents the Distance Formula to find the length of a segment on the coordinate plane?
A
$PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
B
$PQ = \sqrt{(x_2 + x_1)^2 + (y_2 + y_1)^2}$
C
PQ = (x2 - x1 )2 + (y2 - y1 )2
D
$PQ = \sqrt{(x_2 - x_1)^2 - (y_2 - y_1)^2}$
Explanation
The distance formula is derived from the Pythagorean theorem and is correctly represented as the square root of the sum of the squared differences of the x and y coordinates.
🚩 Report
Find the distance between
J(4, 3) and
K(-3, -7) .
A
$\sqrt{13}$
B
$\sqrt{149}$
C
$\sqrt{65}$
D
$\sqrt{17}$
Explanation
Using the formula $d = \sqrt{(-3-4)^2 + (-7-3)^2} = \sqrt{(-7)^2 + (-10)^2} = \sqrt{49 + 100} = \sqrt{149}$.
🚩 Report
Find the distance between the pair of points shown on the grid.
Explanation
The points are V(5, 7) and U(-1, -1) . $d = \sqrt{(5 - (-1))^2 + (7 - (-1))^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$.
🚩 Report
Find the distance between the pair of points shown on the grid.
A
$\sqrt{35} \approx 5.92$
B
$\sqrt{40} \approx 6.32$
C
$\sqrt{45} \approx 6.71$
D
$\sqrt{50} \approx 7.07$
Explanation
The points are M(4, 0) and L(-2, -3) . $d = \sqrt{(4 - (-2))^2 + (0 - (-3))^2} = \sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.71$.
🚩 Report
Find the distance between the pair of points shown on the grid.
A
$\sqrt{73} \approx 8.54$
B
$\sqrt{80} \approx 8.94$
C
$\sqrt{89} \approx 9.43$
D
$\sqrt{97} \approx 9.85$
Explanation
The points are J(-3, 4) and K(2, -4) . $d = \sqrt{(2 - (-3))^2 + (-4 - 4)^2} = \sqrt{5^2 + (-8)^2} = \sqrt{25 + 64} = \sqrt{89} \approx 9.43$.
🚩 Report
Find the distance between A(2, 6) and N(5, 10) .
Explanation
$d = \sqrt{(5 - 2)^2 + (10 - 6)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.
🚩 Report
Find the distance between R(3, 4) and T(7, 2) .
A
$\sqrt{12} \approx 3.46$
B
$\sqrt{18} \approx 4.24$
C
$\sqrt{20} \approx 4.47$
D
$\sqrt{24} \approx 4.90$
Explanation
$d = \sqrt{(7 - 3)^2 + (2 - 4)^2} = \sqrt{4^2 + (-2)^2} = \sqrt{16 + 4} = \sqrt{20} \approx 4.47$.
🚩 Report
Find the distance between X(-3, 8) and Z(-5, 1) .
A
$\sqrt{41} \approx 6.40$
B
$\sqrt{49} = 7$
C
$\sqrt{53} \approx 7.28$
D
$\sqrt{61} \approx 7.81$
Explanation
$d = \sqrt{(-5 - (-3))^2 + (1 - 8)^2} = \sqrt{(-2)^2 + (-7)^2} = \sqrt{4 + 49} = \sqrt{53} \approx 7.28$.
🚩 Report
Find the distance between M(-4, 9) and N(-5, 3) . Round to the nearest tenth.
A
$\sqrt{13}$ or about 3.6 units
B
$\sqrt{37}$ or about 6.1 units
C
$\sqrt{85}$ or about 9.2 units
D
$\sqrt{45}$ or about 6.7 units
Explanation
$d = \sqrt{(-5 - (-4))^2 + (3 - 9)^2} = \sqrt{(-1)^2 + (-6)^2} = \sqrt{1 + 36} = \sqrt{37} \approx 6.1$.
🚩 Report
Find the distance between C(2, 4) and D(5, 7) . Round to the nearest tenth.
A
$\sqrt{58}$ or about 7.6 units
B
$\sqrt{18}$ or about 4.2 units
C
$\sqrt{10}$ or about 3.2 units
D
$\sqrt{20}$ or about 4.5 units
Explanation
$d = \sqrt{(5 - 2)^2 + (7 - 4)^2} = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} \approx 4.2$.
🚩 Report
Find the distance between A(5, 1) and B(3, 6) . Round to the nearest tenth.
A
$\sqrt{17}$ or about 4.1 units
B
$\sqrt{29}$ or about 5.4 units
C
$\sqrt{13}$ or about 3.6 units
D
$\sqrt{41}$ or about 6.4 units
Explanation
$d = \sqrt{(3 - 5)^2 + (6 - 1)^2} = \sqrt{(-2)^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.4$.
🚩 Report
Find the distance between V(4, 4) and X(5, 8) . Round to the nearest tenth.
A
$\sqrt{29}$ or about 5.4 units
B
$\sqrt{17}$ or about 4.1 units
C
$\sqrt{5}$ or about 2.2 units
D
$\sqrt{25}$ or about 5.0 units
Explanation
$d = \sqrt{(5 - 4)^2 + (8 - 4)^2} = \sqrt{1^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.1$.
🚩 Report
Find the distance between S(6, 4) and T(3, 2) . Round to the nearest tenth.
A
$\sqrt{37}$ or about 6.1 units
B
$\sqrt{13}$ or about 3.6 units
C
$\sqrt{45}$ or about 6.7 units
D
$\sqrt{17}$ or about 4.1 units
Explanation
$d = \sqrt{(3 - 6)^2 + (2 - 4)^2} = \sqrt{(-3)^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} \approx 3.6$.
🚩 Report
Find the distance between M(-1, 8) and N(-3, 3) . Round to the nearest tenth.
A
$\sqrt{18}$ or about 4.2 units
B
$\sqrt{29}$ or about 5.4 units
C
$\sqrt{13}$ or about 3.6 units
D
$\sqrt{41}$ or about 6.4 units
Explanation
$d = \sqrt{(-3 - (-1))^2 + (3 - 8)^2} = \sqrt{(-2)^2 + (-5)^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.4$.
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