Geometry Answers

Ms. Flair teaches art. She keeps her paintbrushes in a crate that is shaped like a cube The crate measures 10 inches on each side. What is the volume of Ms. Flairs crate

If K is the midpoint of JL, JK = 8x+11 and KL = 14x-1, find JL

You are interesting in a buying a gift that is shaped like a cube for your fruend.However,you only have a 5 square yards of wrapping paper.the formula is s=√A-6 where s is the edge length,and A is the surface area.What is the longest side length of a cube you could buy based on how much wrapping paper you have?round your answer to the nearest tenth of a yard?

Department of Mathematics University of Ghana Math123: Vectors and Geometry Module 4: Exercise 3 Module 4 (Lines in Space)

TK/GAB/JB/EKAS/KD/JDGM 15/02/2021

Consider the line l1 joining the points A(−5, −3, 0) and B(7, 1, 4).

1. Find the parametric equation of the line.

2. Show that the point C(1, −1, 2) lies on the line.

3. Show that the point D(−4, 3, 2) is not on the line.

4. Find the foot of the perpendicular Q from D to the line and determine the shortest distance between the point and the line.

5. Thelinel1 intersectsthelinel2 givenbyr=12i−3j+4k+μ􏰀−8i+3j−k􏰁.

(a) Find the position vector of the point R of intersection.

(b) Find the angle between the two lines.

(c) Find the equations of the internal and external bisectors of the angle between the

 lines l1 and l2.

(d) The point D is on l2. Find a point D′ such that DQ = QD′.

(e) Find the equation of the line l2′ joining R and D′.

(f) Show that l1 is the bisector of angle DRD′. [Line l2′ is the mirror image of the line l2 in l1]

Figure 1:

−→ −−→

 1

A stained glass window in a museum is in the shape of a rectangle with a semicircle on top. The height of the rectangle part of the window is twice the base. If the base of the window is 12 feet, what is the area of the window ?

Using the circle graph that you have made, formulate at least two problems involving arcs and central angles, then solve.

Congruence and Triangles/ Complete each statement by naming the corresponding angle or side

The three non-parallel edges of a rectangular solid are in the ratio 1 : 2 : 3. The diagonal of the solid is 2√14m. Find the length of the longest side.

The base of the prism is a rhombus of side 20 cm with one diagonal 24 cm. Find the area of the base.

The basal edge is 6 cm. of the regular triangular prism. What is the area of the base?