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3 years ago

Which step should be taken next to construct a line through point P perpendicular to BA?

Mathematics

2 answers:

Pavel [41]3 years ago

8 0

Answer:

Refer picture enclosed

Step-by-step explanation:

Given is a line BA and a point P. We have to construct a line perpendicular to BA through P.

Case I: P lies on the line BA

Without loss of generality assume BP is smaller than AP.

Cut an arc C on AB from P such that BP=CP

Now with B and C as centres draw arc up and down the line with more than half length of BC

Join the intersecting of arcs. That line is the perpendicular for BA through P.

This is because of concurrency of two triangles above the line BC

Case2:

P lies outside the line. Measure PB and cut an arc of BA with length PB

Let the point be C

Then CP=BP

NOw do as we did before the line with arcs more than 1/2 length of BC from B and C only down. Join the point of intersection down with P. This line will be perpendicular through P to BA

lesya [120]3 years ago

3 0

Answer: place the compass on point A. Open the compass to a point somewhere between point P and point B

ON GRADPOINT.

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Francesca leaves her home and Drive South 150 km. Then she drives West 70 km. At this point, she drives North 30 km. Finally, sh

Sveta_85 [38]

To find the distance between her home and her latest position:

According to the question, the diagram is,

Consider the right triangle,

AB=120 km

BC=50 km

To find AC:

Using Pythagoras theorem,

$\begin{gathered} AC^2=AB^2+BC^2_{} \\ =120^2+50^2 \\ =14400+2500 \\ =16900 \\ =130\text{ km} \end{gathered}$

Hence, the distance between the new position and her home is 130 km.

8 0

1 year ago

Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)

Blizzard [7]

Answer:

One possible equation is $f(x) = (x + 3)\, (x - 5)$ , which is equivalent to $f(x) = x^{2} - 2\, x - 15$ .

Step-by-step explanation:

The factor theorem states that if $x = x_{0}$ (where $x_{0}$ is a constant) is a root of a function, $(x - x_{0})$ would be a factor of that function.

The question states that $(-3,\, 0)$ and $(5,\, 0)$ are $x$ -intercepts of this function. In other words, $x = -3$ and $x = 5$ would both set the value of this quadratic function to $0$ . Thus, $x = -3\!$ and $x = 5\!$ would be two roots of this function.

By the factor theorem, $(x - (-3))$ and $(x - 5)$ would be two factors of this function.

Because the function in this question is quadratic, $(x - (-3))$ and $(x - 5)$ would be the only two factors of this function. In other words, for some constant $a$ ( $a \ne 0$ ):

$f(x) = a\, (x - (-3))\, (x - 5)$ .

Simplify to obtain:

$f(x) = a\, (x + 3)\, (x - 5)$ .

Expand this expression to obtain:

$f(x) = a\, (x^{2} - 2\, x - 15)$ .

(Quadratic functions are polynomials of degree two. If this function has any factor other than $(x - (-3))$ and $(x - 5)$ , expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of $a$ corresponds to a distinct quadratic function with $x$ -intercepts $(-3,\, 0)$ and $(5,\, 0)$ . For example, with $a = 1$ :