Coordinate Proofs

Question 1

ABCD is graphed on the coordinate plane. What slope evidence proves ABCD is a parallelogram?

Accepted Answer

Slopes AB and CD are both 1/2, and slopes BC and AD are both 2.

Answer

Slopes AB and BC are both 1/2, and slopes CD and AD are both 2.

Answer

Slopes AB and AD are both 2, and slopes BC and CD are both 1/2.

Answer

Slopes AC and BD are both 1, and slopes AB and CD are both 1/2.

Question 2

Points A, B, C, and D are shown on the coordinate plane. What slope evidence proves angle ABC is a right angle?

Accepted Answer

Slope BA is 1/2 and slope BC is -2.

Answer

Slope BA is 2 and slope BC is -1/2.

Answer

Slope BA is 1/2 and slope CD is 1/2.

Answer

Slope BA is -2 and slope BC is 1/2.

Question 3

The coordinate plane shows quadrilateral ABCD. What slope evidence proves one pair of opposite sides is parallel?

Accepted Answer

Slopes AB and CD are both 0.

Answer

Slopes AD and BC are both 3.

Answer

Slopes AB and AD are both 0.

Answer

Slopes AC and BD are both 3/4.

Question 4

In quadrilateral ABCD as graphed, what slope evidence proves ABCD is a parallelogram?

Accepted Answer

Slopes AB and CD are both 0, and slopes BC and AD are both 3/2.

Answer

Slopes AB and BC are both 0, and slopes CD and AD are both 3/2.

Answer

Slopes AB and CD are both 3/2, and slopes BC and AD are both 0.

Answer

Slopes AC and BD are both 3/7, and slopes AB and CD are both 0.

Question 5

The vertices of ABCD are plotted on the coordinate plane. What slope evidence proves diagonals AC and BD are perpendicular?

Accepted Answer

Slope AC is undefined and slope BD is 0.

Answer

Slope AB is -3/4 and slope CD is -3/4.

Answer

Slope AD is 3/4 and slope BC is 3/4.

Answer

Slope AC is 0 and slope BD is undefined.

Question 6

Triangle ABC is drawn on the coordinate plane. What slope evidence proves angle BAC is a right angle?

Accepted Answer

Slope AB is 1/2 and slope AC is -2.

Answer

Slope AB is 2 and slope AC is -1/2.

Answer

Slope AB is 1/2 and slope BC is -1/3.

Answer

Slope AB is -2 and slope AC is 1/2.

Question 7

The plotted points form ABCD. What slope evidence proves ABCD is a parallelogram?

Accepted Answer

Slopes AB and CD are both 4/3, and slopes BC and AD are both 0.

Answer

Slopes AB and AD are both 4/3, and slopes BC and CD are both 0.

Answer

Slopes AB and BC are both 4/3, and slopes CD and AD are both 0.

Answer

Slopes AC and BD are both 1/2, and slopes BC and AD are both 0.

Question 8

Triangle ABC is shown on the coordinate plane. What distance evidence proves the triangle is isosceles?

Accepted Answer

AC = 5 units and BC = 5 units.

Answer

AB = 6 units and AC = 6 units.

Answer

AB = 5 units and BC = 5 units.

Answer

AC = 13 units and BC = 13 units.

Question 9

The coordinate plane shows ABCD. What distance evidence proves all sides are congruent?

Accepted Answer

AB = 5 units, BC = 5 units, CD = 5 units, and DA = 5 units.

Answer

AB = 3 units, BC = 3 units, CD = 3 units, and DA = 3 units.

Answer

AB = 4 units, BC = 4 units, CD = 4 units, and DA = 4 units.

Answer

AB = 5 units, BC = 3 units, CD = 5 units, and DA = 3 units.

Question 10

A coordinate-plane figure shows triangle ABC. What distance evidence proves the triangle is isosceles?

Accepted Answer

AC = 13 units and BC = 13 units.

Answer

AB = 4 units and AC = 4 units.

Answer

AB = 13 units and BC = 13 units.

Answer

AC = 5 units and BC = 5 units.

Question 11

Triangle ABC is plotted on the coordinate plane. What distance evidence proves the triangle is scalene?

Accepted Answer

AB = 17 units, AC = 26 units, and BC = 5 units.

Answer

AB = 17 units, AC = 17 units, and BC = 5 units.

Answer

AB = 5 units, AC = 26 units, and BC = 5 units.

Answer

AB = 26 units, AC = 26 units, and BC = 5 units.

Question 12

ABCD is shown on the coordinate plane. What distance evidence proves opposite sides of ABCD are congruent?

Accepted Answer

AB = CD = 5 units, and BC = AD = 2 units.

Answer

AB = BC = 5 units, and CD = AD = 2 units.

Answer

AB = AD = 5 units, and BC = CD = 2 units.

Answer

AB = CD = 2 units, and BC = AD = 5 units.

Question 13

The coordinate plane shows triangle ABC. What distances prove the triangle has two congruent legs?

Accepted Answer

AB = 5 units and AC = 5 units.

Answer

AB = 5 units and BC = 5 units.

Answer

AC = 52 units and BC = 52 units.

Answer

AB = 26 units and AC = 26 units.

Question 14

A coordinate proof needs to show ABCD has four congruent sides. What side-distance evidence works?

Accepted Answer

AB = BC = CD = DA = 13 units.

Answer

AB = BC = CD = DA = 5 units.

Answer

AB = CD = 13 units and BC = DA = 5 units.

Answer

AB = BC = 5 units and CD = DA = 13 units.

Question 15

ABCD is graphed. What midpoint evidence proves the diagonals bisect each other?

Accepted Answer

Midpoint AC = (2, 1) and midpoint BD = (2, 1).

Answer

Midpoint AB = (1, 3) and midpoint CD = (3, -1).

Answer

Midpoint AC = (2, 1) and midpoint AB = (1, 3).

Answer

Midpoint BD = (2, 1) and midpoint CD = (3, -1).

Question 16

Quadrilateral ABCD is graphed on the coordinate plane. What midpoint evidence proves ABCD is a parallelogram?

Accepted Answer

Midpoint AC = (3, 2) and midpoint BD = (3, 2).

Answer

Midpoint AB = (2, 0) and midpoint CD = (4, 4).

Answer

Midpoint AD = (1, 2) and midpoint BC = (5, 2).

Answer

Midpoint AC = (3, 2) and midpoint AB = (2, 0).

Question 17

Nolan wants to prove ABCD is a parallelogram by diagonals. What midpoint evidence completes the proof?

Accepted Answer

Midpoint AC = (0, 2) and midpoint BD = (0, 2).

Answer

Midpoint AB = (-2, 3) and midpoint CD = (2, 1).

Answer

Midpoint AC = (0, 2) and midpoint AB = (-2, 3).

Answer

Midpoint BD = (0, 2) and midpoint CD = (2, 1).

Question 18

For the graphed quadrilateral ABCD, what midpoint evidence shows the diagonals bisect each other?

Accepted Answer

Midpoint AC = (3, 1) and midpoint BD = (3, 1).

Answer

Midpoint AB = (3.5, -1) and midpoint CD = (2.5, 3).

Answer

Midpoint AD = (0.5, 0) and midpoint BC = (5.5, 2).

Answer

Midpoint AC = (3, 1) and midpoint AB = (3.5, -1).

Question 19

A proof should show the graphed quadrilateral ABCD is not a parallelogram. What midpoint evidence shows the diagonals do not bisect each other?

Accepted Answer

Midpoint AC = (2, 1.5) and midpoint BD = (3, 1.5).

Answer

Midpoint AC = (2, 1.5) and midpoint BD = (2, 1.5).

Answer

Midpoint AB = (2.5, 0) and midpoint CD = (2.5, 3).

Answer

Midpoint AC = (3, 1.5) and midpoint BD = (2, 1.5).

Question 20

For quadrilateral ABCD, what midpoint evidence proves ABCD is a parallelogram?

Accepted Answer

Midpoint AC = (1, -1) and midpoint BD = (1, -1).

Answer

Midpoint AB = (-1, -3) and midpoint CD = (3, 1).

Answer

Midpoint AD = (-1, 0) and midpoint BC = (3, -2).

Answer

Midpoint AC = (1, -1) and midpoint AB = (-1, -3).

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Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner

Coordinate Proofs

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner