SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Cartesian Plane, SMB-016

Calculate the value(s) of `p` given that the points `(p,3)` and `(1,p)` are exactly 10 units apart.  (3 marks)

Show Answers Only

`p=9\ text{or}\ -5`

Show Worked Solution

`(p,3),\ \ (1,p)`

`text{Using the distance formula:}`

`d` `=sqrt{(x_2-x_1)^2+(y_2-y_1)^2}`  
`10` `=sqrt{(p-1)^2+(3-p)^2}`  
`10` `=sqrt{p^2-2p+1+9-6p+p^2}`  
`10` `=sqrt{2p^2-8p+10}`  
`100` `=2p^2-8p+10`  
`0` `=2p^2-8p-90`  
`0` `=p^2-4p-45`  
`0` `=(p-9)(p+5)`  

 
`:.p=9\ text{or}\ -5`

Cartesian Plane, SMB-015

Calculate the distance between the points `(2,-3)` and `(-5,4)`.

Round your answer to the nearest tenth.  (2 marks)

Show Answers Only

`9.9\ text{units}`

Show Worked Solution

`(2,-3),\ \ (-5,4)`

`text{Using the distance formula:}`

`d` `=sqrt{(x_2-x_1)^2+(y_2-y_1)^2}`  
  `=sqrt{(2-(-5))^2+(-3-4)^2}`  
  `=sqrt{49+49}`  
  `=sqrt{98}`  
  `=9.899…`  
  `=9.9\ text{units (nearest tenth)}`  

Cartesian Plane, SMB-014

Calculate the distance between the points `(6,-5)` and `(0,3)`.  (2 marks)

Show Answers Only

`10\ text{units}`

Show Worked Solution

`(6,-5),\ \ (0,3)`

`text{Using the distance formula:}`

`d` `=sqrt{(x_2-x_1)^2+(y_2-y_1)^2}`  
  `=sqrt{(6-0)^2+(-5-3)^2}`  
  `=sqrt{36+64}`  
  `=sqrt{100}`  
  `=10\ text{units}`  

Cartesian Plane, SMB-013

Calculate the distance between the point `(-6,2)` and the origin.

Give your answer in exact form.  (2 marks)

Show Answers Only

`2sqrt{10}\ \ text{units}`

Show Worked Solution

`(-6,2),\ \ (0,0)`

`text{Using the distance formula:}`

`d` `=sqrt{(x_2-x_1)^2+(y_2-y_1)^2}`  
  `=sqrt{(-6-0)^2+(2-0)^2}`  
  `=sqrt{36+4}`  
  `=sqrt{40}`  
  `=2sqrt{10}\ \ text{units}`