Geometry

Question 1

If given 3 points, what information do you need to find to determine the type of triangle? What does this information tell you?

Answer 1

1) The length of each side
2) The slope of each side

If all 3 sides have the same side lengths and slope the triangle is an equilateral

If 2 sides have the same side lengths and slope the triangle is an isosceles

If all sides has different side lengths and slopes the triangle is a scalene

Question 2

Midpoint

Answer 2

The point that divides a line segment into 2 equal segments

Question 3

Median

Answer 3

The line segment joining a vertex of a triangle to the midpoint of the opposite side.

Question 4

How do you find the equation of a median?

Answer 4

Step 1) Find the midpoint

Step 2) Find the slope of the median

Step 3) Pick point A or midpoint

Step 4) y= mx+b

Question 5

What is Altitude?

Answer 5

A line sement drawn for a vertex perpendicular to the opposite side

Question 6

How do you determine the equation of an altitude?

Answer 6

Step 1) Find the slope of BC

Step 2) Turn it into the Negative Reciprocal (slope of AH)

Step 3) Use the remaining point and slope and sub them into y= mx+b

Question 7

What is the equation for Pythagorean Theorem?​

Answer 7

a²+b²=c²

*A AND B ARE THE LENGTH OF THE LEGS AND C IS THE LENGTH OF THE HYPOTENEUSE*

Question 8

What is the equation for the area of a circle?

Answer 8

a= ¶r²

Question 9

What is the Perpendicuar Bisector of a Side?

Answer 9

A line segment that passes through the midpoint at 90º

Question 10

How do you find the equation of a perpendicular bisector of a side?

Answer 10

Step 1) Find the slope of BC

Step 2) Negative Reciprocal= Slope of right bisector

Step 3) Find the midpoint of BC

Step 4) y=mx+b

Question 11

What is the equation for the Distance to the Origin From Any Point?

Answer 11

Question 12

What is the equation for the Distance Between Any 2 Points?

Answer 12

Question 13

What is the equation for the Equation of a Circle, Centre (0,0) and Radius r?

Answer 13

x²+ y²=r²

Question 14

What is the equation of the Midpoint of a Line Segment With Endpoints?

Answer 14

Question 15

When given a point, how do you determine if it is inside, outside or on the circle?

Answer 15

Substitute the point into the equation and solve

1) If both sides of the equation are equal, the point is on the circle
2) If the left side of the equation is smaller it is inside the circle
3) If the left side is larger it is outside the circle

Question 16

How do you classify a shape when given coordinates?

Answer 16

Find the slope and/ or length of each side

Question 17

If given the equation x²+y²=169 answer the following:

a) The coodinates of the centre
b) The length of the radius
c) The x-intercept(s)
d) The coordinates of a point on the circle, but not on the x or y axis

Answer 17

a) (0,0)
b) Square Root of 169= 13

*SQUARE ROOT THE NUMBER AFTER THE EQUAL SIGN*

c) (13,0) (-13,0)

*TAKE THE NUMBER FROM B AND PUT A 0 AFTER IT, DO THE SAME FOR THE NEXT POINT BUT MAKE IT NEGATIVE*

d) (12,5)

*GUESS AND CHECK, SUB POINTS INTO THE EQUATION AND CHECK*