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Secondary 4
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Geometry and Measurement

Construct
A) the perpendicular bisector of side AB
B) the angle bisector of angle BCD

Replies
12

Mr. T

Bisector of line AB means a special line that cuts across AB separating line AB into 2 EQUAL parts.
Perpendicular means this special line is at right angles or 90 degrees to line AB.
So check this special line is passes the midpoint on line AB by measuring AM equals BM.

1 year ago

Mr. T

Step 1: Place your compass with pointer( the sharp end) on point A.

1 year ago

Mr. T

Step 2: Adjust compass to be MORE THAN HALF the length of AB.

1 year ago

Mr. T

Step 3: Draw arc to be above and below the line AB.

1 year ago

Mr. T

Repeat the same for point B, see Step 1, 2 and 3 and do for point B.

1 year ago

Mr. T

Step 4: Join the top and bottom points where the arcs meet.
(a) is the perpendicular bisector.Hooray.
Check (I): AM is same length as BM. Use ruler on AM and on BM, they should be same length.
Check (II): Your newly constructed perpendicular bisector (a) is at right angles, or 90 degrees to AB. Use a protractor for this check.

1 year ago

Mr. T

Angle bisector refers to dividing into two equal parts.

1 year ago

Mr. T

It is dividing the angle BCD into 2 equal parts

1 year ago

Mr. T

Angle BCD refers to angle C. Always look at the MIDDLE alphabet to know which angle they are asking. This case BCD..C is the MIDDLE alphabet and so C is the angle they ask for.

1 year ago

Mr. T

Step 1: Put the sharp end of your compasses at point C and make one arc on the line BC (point S) and another arc on line CD (point T).

1 year ago

Mr. T

Step 2: Put the sharp end of the compasses at S and make an arc within the lines BC and CD. Do the same at T and make sure that the second arc intersects the first arc.

1 year ago

Mr. T

(b) is your angle bisector.Hooray.
Check: Use a protractor for angle BC(b) and angle DC(b), they must be equal and so angle BCD is bisected.

Can you rewrite the second part evaluate...cannot be seen properly.

1 year ago

Mr. T

Binomial expansion of (2-x)^4
YKTYR EAL
Can you show step by step to a student (2-x)^4 this binomial expansion
Yes, I can definitely help you with that!
The binomial expansion of (a + b)^n can be expressed using the formula:
(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n
where nCk represents the binomial coefficient and is given by the formula:
nCk = n! / (k! * (n-k)!)
Now, let's apply this formula to expand (2 - x)^4:
(2 - x)^4 = 4C0 * 2^4 * (-x)^0 + 4C1 * 2^3 * (-x)^1 + 4C2 * 2^2 * (-x)^2 + 4C3 * 2^1 * (-x)^3 + 4C4 * 2^0 * (-x)^4
Simplifying each term using the binomial coefficient formula:
= 1 * 2^4 * 1 + 4 * 2^3 * (-x) + 6 * 2^2 * x^2 + 4 * 2^1 * (-x)^3 + 1 * 2^0 * x^4
= 16 - 32x + 24x^2 - 8x^3 + x^4
Therefore, the binomial expansion of (2 - x)^4 is 16 - 32x + 24x^2 - 8x^3 + x^4.

1 year ago

Mr. T

The binomial expansion of (a + b)^n can be expressed using the formula:
(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n
where nCk represents the binomial coefficient and is given by the formula:
nCk = n! / (k! * (n-k)!)