Length of a line segment questions with answers

Questions

1. Question 1Whole-number lengths

   Find the length of the line segment joining $A(2, 3)$ and $B(-1, -1)$.

   Show the worked solution

   1. Step 1: Put the coordinates into the length formula$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$AB = \sqrt{(-1 - 2)^2 + (-1 - 3)^2}$$= \sqrt{25}$
   2. Step 2: Work out the square root$AB = 5$ units
2. Question 2To 3 significant figures

   Find the length of the line segment joining $A(-1, 1)$ and $B(0, 2)$, correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Put the coordinates into the length formula$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$AB = \sqrt{(0 - (-1))^2 + (2 - 1)^2}$$= \sqrt{2}$
   2. Step 2: Work out the square root, then round$AB = 1.4142\ldots$$\phantom{AB} = 1.41$ units (3 s.f.)
3. Question 3Find a missing coordinate

   The distance between $A(-2, k)$ and $B(2, 5)$ is $5$ units. Find the two possible values of $k$.

   Show the worked solution

   1. Step 1: Use Pythagoras with k$(2 - (-2))^2 + (5 - k)^2 = 5^2$$(5 - k)^2 = 25 - 16$$= 9$
   2. Step 2: Take ± the square root$5 - k = \pm 3$$k = 2$ or $k = 8$
4. Question 4Perimeter of a triangle

   Triangle $ABC$ has vertices $A(-3, -1)$, $B(6, 3)$ and $C(2, -3)$. Find the perimeter of the triangle, correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Find each side with Pythagoras$AB = \sqrt{81 + 16}$$\phantom{AB} = 9.8488\ldots$$BC = \sqrt{16 + 36}$$\phantom{BC} = 7.2111\ldots$$CA = \sqrt{25 + 4}$$\phantom{CA} = 5.3851\ldots$
   2. Step 2: Add, then roundPerimeter $= 22.4451\ldots$$= 22.4$ units (3 s.f.)