Coordinate Geometry

Question 1

Median

Answer 1

Vertices to the midpoint of opposite side

Question 2

Altitude

Answer 2

Perpendicular to the opposite side

Question 3

Perpendicular Bisector

Answer 3

Cuts opposite side in half but does not have to come from Vertice

Question 4

Write an equation of line parallel to 5x-8y+2=0 with coordinates (-1,7)

Answer 4

Y-7 = 5/8 (x-1) (x+1??)

Question 5

How to find a value collinear to other values?

Answer 5

Find the average (median) of the other 2 values

Question 6

Bh/2

Answer 6

Area of a triangle

Question 7

Sum of the lengths of the 3 sides

Answer 7

Perimeter of a triangle

Question 8

2
S, 4s

Answer 8

Area & Perimeter of a square

Question 9

A= bh (lw)

Answer 9

Area of a rectangle, rhombus, or parallelogram

Question 10

Perimeter of a rectangle, rhombus, and/or parallelogram

Answer 10

P= 2b+ 2h

Question 11

How to prove a triangle is scalene

Answer 11

Use distance formula 3 times to prove each side has a different length

Question 12

How to prove a triangle is isosceles

Answer 12

Distance formula 3 times to prove 2 sides are congruent

Question 13

How to prove a triangle is equilateral

Answer 13

Distance formula 3 times to prove all 3 sides are equal to each other

Question 14

How to prove a right triangle

Answer 14

Use slope formula 3 times to prove 2 sides are perpendicular (the slopes will be negative reciprocals of the other)

Question 15

How to prove a parallelogram is a quadrilateral

Answer 15

Use slope formula 4 times to prove both pairs of opposite sides are parallel

Question 16

How to prove a rectangle is a quadrilateral

Answer 16

Use slope formula 4 times to prove it’s a parallelogram and consecutive sides are perpendicular

Question 17

How to prove a rhombus is a quadrilateral

Answer 17

Use slope formula 6 times (4 for each side + diagonals) to prove it’s a parallelogram (both pairs of opposite sides are parallel) and diagonals are perpendicular to each other

Question 18

How to prove a square is a quadrilateral

Answer 18

Slope formula 6 times to prove it’s a parallelogram, 2 consecutive sides are perpendicular and diagonals are perpendicular (prove it’s a parallelogram, rectangle, and rhombus)

Question 19

How to prove a trapezoid is a quadrilateral

Answer 19

Use slope formula 4 times to prove at least one pair of opposite sides are parallel

Question 20

How to prove an isosceles trapezoid is a parallelogram

Answer 20

Slope formula 4x and distance formula 2x to prove it’s a trapezoid and either the non parallel sides or diagonals are equal

Question 21

Proof an isosceles trapezoid is a parallelogram

Answer 21

prove it’s a trapezoid and either the non parallel sides or diagonals are equal

Question 22

Prove a trapezoid is a quadrilateral

Answer 22

prove at least one pair of opposite sides are parallel

Question 23

Prove a square is a quadrilateral

Answer 23

prove it’s a parallelogram, 2 consecutive sides are perpendicular and diagonals are perpendicular (prove it’s a parallelogram, rectangle, and square)

Question 24

Prove a rhombus is a quadrilateral

Answer 24

prove it’s a parallelogram (both pairs of opposite sides are parallel) and diagonals are perpendicular to each other

Question 25

Prove a rectangle is a quadrilateral

Answer 25

prove it’s a parallelogram and consecutive sides are perpendicular!!!

Question 26

Prove a parallelogram is a quadrilateral

Answer 26

prove both pairs of opposite sides are parallel

Question 27

how to do a question in which it gives 3 points with a variable and asks to prove something is a right triangle

Answer 27

1) find slope of coordinates w/out variable
2) find negative reciprocal of this slope and set equal to one of the coordinates with said variable
3) division, multiplication, etc. until x=

Question 28

How to find median (random pair of coordinates from line with slope, made up from vertex & midpoint of that line)

Answer 28

1) find MIDPOINT!!!! of the line the median intersects
2) take those coordinates + the vertex’s coordinates to find slope of the median
3) use THIS SLOPE and a RANDOM pair of coordinates from the line to set up the equation

Question 29

How to find altitude (slope of line, flipped and negated, with vertex of triangle)

Answer 29

1) find slope of the side the altitude intersects and flip & negate it
2) Use the vertex (where altitude begins) and the slope to set up an equation

Question 30

How to find perpendicular bisector (flipped and negated slope of the line and the midpoint’s coordinates)

Answer 30

1) Find side of the slope the side that is bisected and flip & negate it
2) FIND MIDPOINT OF THE SIDE THAT WAS BISECTED !!
3) use the midpoint of that side and slope to set up equation

Question 31

Setting up equations

Answer 31

Median: random point from the line & slope (using vertex and midpoint of line as coordinates for slope)
Altitude: slope of line that’s flipped and negated with the coordinates of the vertex
Perpendicular Bisector: slope of line that’s flipped and negated + the midpoint of that same line

Question 32

area of a trapezoid

Answer 32

a+b/
2h

Question 33

area of an isosceles trapezoid

Answer 33

Area = 1/2 (a+b) (h)