Answer:
10.7 feet
Step-by-step explanation:
The ladder, the ground and the wall form the shape of a right angled triangle as shown in the image below.
The hypotenuse of the triangle is 14 feet (length of ladder)
The base of the triangle is 9 feet long (the distance from the base of the ladder to the wall)
We need to find the height of the triangle. We can apply Pythagoras rule:
where hyp = hypotenuse
a = base of the triangle
b = height of the triangle
Therefore:
The wall reaches 10.7 feet high.
Answer: By the slope formula.
Step-by-step explanation:
Given: ABC is a triangle (shown below),
In which A≡(6,8), B≡(2,2) and C≡(8,4)
And, D and E are the mid points of the line segments AB and BC respectively.
Prove: DE║AC and DE = AC/2
Proof:
Since, And, D and E are the mid points of the line segments AB and BC respectively.
Therefore, By mid point theorem,
coordinate of D are
Coordinate of E are
By the distance formula,
By the slope formula,
Slope of AC =
Slope of DE =
Statement Reason
1. The coordinate of D are (4,5) and 1. By the midpoint formula
the coordinate of E are (5,3)
2. The length of DE = √5 2. By the Distance formula
The length AC = 2√5 ⇒ Segment DE
is half the length of segment AC
3. The slope of DE = -2 and the 3. By the slope formula
slope of AC = -2
4. DE║AC 4. Slopes of parallel lines are equal
