If you cut a triangle out of a piece of paper, and move that triangle around (sliding, rotating, reflecting) then that triangle will retain its original shape and size. The three movement types mentioned are rigid motions. They do not change the size or shape of the triangle. If two triangles are congruent, then a sequence of one or more rigid motions can be applied to have them line up together.
absolute value is 8 because the absolute value of a negative is positive and the absolute value of positive stays positive
Answer:
Step-by-step explanation:
Since MNP is equilateral, so <PNM=60, and since OP//NM, and <PON is 90, so <MNO=90=<PNM+PNO,so 90=60+<PNO,so <PNO=30
Answer:
b) i) Curve A
ii) - 1.75
iii) x = 1 - √5 or x = 1 + √5
Step-by-step explanation:
b) i) We are given a function y = x² - 2x - 3 and the graph of this function is also shown in the side diagram.
The equation can be rearranged to y = (x - 1)² - 4
⇒ (x - 1)² = y + 4
Therefore, this is an equation of a parabola having the vertex at (1,-4) point and its axis is parallel to the positive y-axis.
So, the curve A represents the equation given. (Answer)
ii) Now, at x = 2.5, f(x) = 2.5² - 2 × 2.5 - 3 = - 1.75 (Answer)
iii) When y = 1, then x² -2x - 3 = 1
⇒ x² - 2x - 4 = 0
⇒ (x - 1)² - 5 = 0
⇒ (x - 1)² - (√5)² = 0
⇒ (x - 1 + √5)(x - 1 - √5) = 0
⇒ x = 1 - √5 or x = 1 + √5 (Answer)
