# Answer in Geometry

Exercise 102

Suppose a ball is dropped from a height of 200m. If time after the ball was released is in seconds, and the height of the ball above the ground at time is given by

, find the average velocity from to

Show that the slope of the line joining the points A(1,1) and B is

A line passes through the points (0, 5) and (9, −1). Find the equation of the line which is perpendicular to the line and passes through its midpoint.

Find the equation of the line that is parallel to the line y = −2x + 6 and passing through the point A(1, 10).

A square has vertices O(0, 0), A(a, 0), B(a, a) and C(0, a).

i Find the midpoint of the diagonals OB and CA.

ii Find the length of a diagonal of the square and the radius of the circle in which OABC is inscribed.

Iii Find the equation of the circle inscribing the square

1. “h(t)=200-10t^2”

“h(2)=200-10(2)^2=160”

“h(3)=200-10(3)^2=110”

The average velocity from 2s to 3s is

“v_{ave}=dfrac{110m-160m}{3s-2s}=-50m/s”

2.

“A(1, 1), B(2, 3+h)”

“slope=dfrac{y_B-y_A}{x_B-x_A}=dfrac{3+h-1}{2-1}=2+h”

3. Midpoint “(9/2, 2)”

“slope_1=dfrac{-1-5}{9-0}=-dfrac{2}{3}”

If line is perpendicular then

“slope_2=-1/(-dfrac{2}{3})=dfrac{3}{2}”

“y=dfrac{3}{2}x+b”

“2=dfrac{3}{2}(dfrac{9}{2})+b=>b=-dfrac{19}{4}”

The equation of the line is

“y=dfrac{3}{2}x-dfrac{19}{4}”

4.

“y=-2x+b”

“10=-2(1)+b=>b=12”

The equation of the line is

“y=-2x+10”

5.

i.

“M(a/2, a/2)”

ii.

“AC=BD=asqrt{2}, >0”

“r=a/2, a>0”

iii.

“R=OB/2=dfrac{sqrt{2}a}{a}, a>0”

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