- Area= 4.5 square units.The area of ΔABC is ^12 its height times
its length, or ^12 (3 ×3). a= 4.5 square units.
Set 96
- In pairs, find each point of interception:
- A (–3,–2). –^13 x– 3 = ^13 x– 1. –^13 x–^13 x= 3 – 1. –^23 x= 2. x= –3;
y= –^13 (–3) – 3. y= 1 – 3. y= –2.
- B (0,–1). ^13 x– 1 = –^13 x– 1. ^13 x+ ^13 x= 1 – 1. ^23 x= 0. x= 0;
y= ^13 (0) – 1. y= –1.
- C (3,–2). –^13 x– 1 = ^13 x– 3. – ^13 x– ^13 x= 1 – 3. –^23 x= –2. x= 3;
y= –^13 (3) – 1. y= –1 – 1. y= –2.
- D (0,–3). ^13 x– 3 = –^13 x– 3. ^13 x+ ^13 x= 3 – 3. ^23 x= 0. x= 0;
y= ^13 (0) – 3. y= –3.- In slope-intercept form, the slope is the constant preceding x. You
can very quickly determine that ABand CD, and BC, and DAhave
the same slopes. The length of each line segment is:
mAB= 10. d= (–3 – 0)^2 + (–2 – –1)^2. d= 9 + 1. d= 10 .
mBC= 10. d= (0 – 3)^2 + (–1– –2)^2. d= 9 + 1. d= 10 .
mCD= 10. d= (3 – 0)^2 + (–2– –3)^2. d= 9 + 1. d= 10 .
mDA= 10. d= (0 – –3)^2 + (–3 – –2)^2. d= 9 + 1. d= 10 .
- The slope of a line is the change in yover the change in x. The
slope of ACis –2–3––(– 3 2), or –^06 . The slope of BDis –1 0 – –(– 0 3), or ^20 .
Lines with zero slopes and no slopes are perpendicular; therefore
diagonals ACand BDare perpendicular. - Rhombus.Quadrilateral ABCD is a rhombus because opposite
sides are parallel, all four sides are congruent, and diagonals are
perpendicular.
501 Geometry Questions