We read your photo as:

Solve the following in English, showing all the steps

English

ScanSolve AI Answer

Answers

3 parts
a
5
b

13\sqrt{13}

c

252\sqrt{5}

Step-by-step solution

10 steps

The formula for the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Part a· 3 steps

Find the length of the line joining $(1,2)$ and $(4,6)$.

  1. Identify the coordinates.

    Let (x1,y1)=(1,2)(x_1, y_1) = (1,2) and (x2,y2)=(4,6)(x_2, y_2) = (4,6).

  2. Substitute the coordinates into the distance formula.

    d=(4−1)2+(6−2)2d = \sqrt{(4 - 1)^2 + (6 - 2)^2}

  3. Simplify the expression.

    d=(3)2+(4)2d = \sqrt{(3)^2 + (4)^2} d=9+16d = \sqrt{9 + 16} d=25d = \sqrt{25} d=5d = \boxed{5}

Part b

13\sqrt{13}

Find the length of the line joining (−1,4)(-1,4) and (2,6)(2,6).

  1. Identify the coordinates.

    Let (x1,y1)=(−1,4)(x_1, y_1) = (-1,4) and (x2,y2)=(2,6)(x_2, y_2) = (2,6).

  2. Substitute the coordinates into the distance formula.

    d=(2−(−1))2+(6−4)2d = \sqrt{(2 - (-1))^2 + (6 - 4)^2}

  3. Simplify the expression.

    d=(2+1)2+(2)2d = \sqrt{(2 + 1)^2 + (2)^2} d=(3)2+(2)2d = \sqrt{(3)^2 + (2)^2} d=9+4d = \sqrt{9 + 4} d=13d = \boxed{\sqrt{13}}

Part c

252\sqrt{5}

Find the length of the line joining (−1,−4)(-1,-4) and (3,−2)(3,-2).

  1. Identify the coordinates.

    Let (x1,y1)=(−1,−4)(x_1, y_1) = (-1,-4) and (x2,y2)=(3,−2)(x_2, y_2) = (3,-2).

  2. Substitute the coordinates into the distance formula.

    d=(3−(−1))2+(−2−(−4))2d = \sqrt{(3 - (-1))^2 + (-2 - (-4))^2}

  3. Simplify the expression.

    d=(3+1)2+(−2+4)2d = \sqrt{(3 + 1)^2 + (-2 + 4)^2} d=(4)2+(2)2d = \sqrt{(4)^2 + (2)^2} d=16+4d = \sqrt{16 + 4} d=20d = \sqrt{20}

  4. Simplify the radical.

    d=4×5d = \sqrt{4 \times 5} d=25d = \boxed{2\sqrt{5}}
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More English Questions

QSolve these in English showing all the steps usedQSolve this in English showing all steps usedQSolve this showing all the steps, in English
See all English questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp