Midpoint and Distance Coordinate Grid

Write a plan for the proof. 

Given: G is the midpoint of HF
Prove: △GHJ≅△GFO

• Find the coordinates of G using the Midpoint Formula
  Use these coordinates and the Distance formula to show that OG ≅ JG.
  Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.
  

• Find the coordinates of G using the Distance Formula
  Use these coordinates and the Midpoint formula to show that OG ≅ JG.
  Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.

• Then, use the SAS Congruence Theorem to conclude that △GHJ ≅ △GFO.

• Then, use the SSS Congruence Theorem to conclude that △GHJ ≅ △GFO.

You and your cousin are camping in the woods. You hike to a point that is 500 meters east and 1200 meters north of the campsite. Your cousin hikes to a point that is 1000 meters east of the campsite.

The distance from you to your cousin is ______ meters.

• 1500

• 1300

• 1200

• 1000

Write a plan for the proof. Given Coordinates of vertices of △OPM and △ONM Prove △OPM and △ONM are isosceles triangles

• Find the lengths of OP, PM, MN, NO and OM to show that △OMP≅△OMN by the SSS Congruence Theorem.

• Find the lengths of OP, PM, MN, and NO to show that OP ≅ PM and MN ≅ NO.

You and your cousin are camping in the woods. You hike to a point that is 500 meters east and 1200 meters north of the campsite. Your cousin hikes to a point that is 1000 meters east of the campsite.

The distance from the campsite to you is ______ meters.

• 1500

• 1300

• 1200

• 1000

Find the coordinates of the vertex O.

• 19

• 8

• 6

• -1.5

• -3

• (7,5)

• (8,6)

• (8,8)

• (10,8)

• (12,10)

Two birds are flying toward a birdhouse that is halfway between them. The birds are at A(-4,4) and B(10,-2). How far will each bird fly to arrive at the birdhouse, if each grid on your graph represents 50ft? Round to the nearest whole number.

You're given point B(3,6) and midpoint C(1,2). What is your missing endpoint A? Write your answer as a coordinate with no spaces.

The endpoints of a diameter of a circle are the points (4,8) and (-6,-2). Where is the center of the circle? Write your answer as a coordinate with no spaces.