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kari74 [83]
3 years ago
9

Find the distance between (-2, 8) and (11, 2). Round to the nearest hundredth.

Mathematics
1 answer:
andrew11 [14]3 years ago
7 0

Answer: 14.32 units

Step-by-step explanation:

The formula for calculate the distance between two points is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

In this case, given the points (-2,8) and (11,2), we can identify that:

x_2=11\\x_1=-2\\\\y_2=2\\y_1=8

Therefore, we just need to substitute values into the formula in order to calculate the distance between the given points. This is (Rounded to the nearest hundred):

d=\sqrt{(11-(-2))^2+(2-8)^2}\\\\d=14.32\ units

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In a problem like this the number that is more to the left is greater. As you can see 0.1 is more to the left

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In Triangle ABC, AC is extended through C to D. If
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Answer:

X  = 5 unit

Step-by-step explanation:

Given as , ABC is a Triangle ,

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∵ <u>External angle = Sum of opposite internal angles</u>

Or ,∠BCD = ∠BAC + ∠ABC

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Read 2 more answers
The bearing of Q from P is 150
Lynna [10]

Answer:

(i) see first attached diagram

(ii) QR = 22.67 km (2 dp)

(iii) 243°

Step-by-step explanation:

A bearing is the angle in degrees measured clockwise from north.

<u />

<u>Part (i)</u>

see first attached diagram

<u>Part (ii)</u>

The angles marked in blue on the second attached diagram are Consecutive Interior Angles.  In this case they add to 180° as the North lines are parallel.

The sum of angles around a point is 360°

⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°        

To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.

⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)

⇒ QR² = 32² + 24² - 2(32)(24)cos(45)

⇒ QR² = 513.8839841...

⇒ QR = √513.8839841...

⇒ QR = 22.67 km (2 dp)

<u>Part (iii)</u>

We need to find the angle marked in green on the third attached diagram.

To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°

Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)

Orange angle (o) using the sine rule:

⇒ sin(o)/32 = sin(45)/QR

⇒ sin(o) = 32sin(45)/22.67

⇒ sin(o) = 0.9981652337...

⇒ o = 86.52868176...°

Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)

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