Problem 1: Horizontal distance
Find the distance between \((2,5)\) and \((9,5)\).
Problem 2: Vertical distance
Find the distance between \((-3,-4)\) and \((-3,6)\).
Problem 3: Draw the legs
Points \(A(1,1)\) and \(B(4,5)\) are plotted. Find the length of \(\overline{AB}\).
Problem 4: Distance from the origin
Find the distance from the origin \((0,0)\) to \((5,12)\).
Problem 5: Two points in Quadrant I
Find the distance between \((2,3)\) and \((10,9)\).
Problem 6: Across quadrants
Find the distance between \(A(-2,-1)\) and \(B(4,7)\).
Problem 7: Moving down and right
Find the distance between \((-7,3)\) and \((5,-2)\).
Problem 8: Distance that is not whole
Find the distance between \((1,1)\) and \((5,6)\). Give the exact value and then round to the nearest tenth.
Problem 9: Larger legs
Find the distance between \((-3,4)\) and \((2,-6)\) to the nearest tenth.
Problem 10: Use the distance formula
Use the distance formula to find the distance between \((-8,-3)\) and \((7,5)\).
Problem 11: Find the error
Liam says the distance between \((1,2)\) and \((4,6)\) is \(3+4=7\). Explain his mistake and find the correct distance.
Problem 12: Which point is closer?
Which point is closer to the origin, \(P(5,-6)\) or \(Q(-7,3)\)? Show the distances.
Problem 13: Missing coordinate
The point \(A(1,2)\) is 10 units from \(B(7,y)\), and \(y\) is greater than 2. Find \(y\).
Problem 14: Perimeter of a grid triangle
Find the perimeter of the triangle with vertices \((0,0)\), \((6,0)\) and \((6,8)\).
Problem 15: Perimeter of a rhombus
Find the perimeter of the quadrilateral with vertices \((0,3)\), \((4,0)\), \((8,3)\) and \((4,6)\).
Problem 16: Perimeter with a slanted side
Find the perimeter of the triangle with vertices \((-4,0)\), \((2,0)\) and \((2,3)\) to the nearest tenth.
Problem 17: Is the triangle isosceles?
Triangle \(ABC\) has vertices \(A(1,1)\), \(B(5,1)\) and \(C(3,5)\). Is it isosceles? Show the three side lengths.
Problem 18: Is the triangle a right triangle?
Triangle \(ABC\) has vertices \(A(1,2)\), \(B(4,6)\) and \(C(8,3)\). Use the three side lengths to decide whether it is a right triangle.
Problem 19: Library to park
On a town map, each grid unit is 1 mile. The library is at \((2,3)\) and the park is at \((8,11)\). How far apart are they in a straight line?
Problem 20: Drone flight
A drone flies in a straight line from \((-4,-3)\) to \((8,2)\) on a grid where each unit is 1 yard. How many yards does it fly?
Problem 21: Home to school
Maya’s house is at \((-3,2)\) and her school is at \((6,-10)\) on a map where each unit is 0.1 mile. How many miles is the straight-line distance?
Problem 22: Fence for a garden
A triangular garden has corners at \((0,0)\), \((9,0)\) and \((9,12)\), where each unit is 1 foot. Fencing costs \$3.50 per foot. How much does the fence around the whole garden cost?
Problem 23: Jogging loop
Jamal jogs a triangular loop around a park with corners at \((0,0)\), \((5,0)\) and \((5,5)\). Each unit is one city block. How many blocks is the loop, to the nearest tenth?
Problem 24: Video game character
In a video game, a character at \((-6,-2)\) runs in a straight line to a flag at \((6,3)\). The character moves 2.6 units per second. How many seconds does the run take?
See every chapter on the Grade 8 math page.