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Point A has coordinates (-4, 6) and point B has coordinates (8, 3) - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

Question 5

Point A has coordinates (-4, 6) and point B has coordinates (8, 3). (a)(i) Find the gradient of line AB. (ii) Find the equation of line AB. (b) Point P has coordi... show full transcript

Worked Solution & Example Answer:Point A has coordinates (-4, 6) and point B has coordinates (8, 3) - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

Step 1

(a)(i) Find the gradient of line AB.

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Answer

To find the gradient of line AB, we use the gradient formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates of points A and B, where A = (-4, 6) and B = (8, 3):

$m = \frac{3 - 6}{8 - (-4)} = \frac{-3}{12} = -\frac{1}{4}$

Thus, the gradient of line AB is $-\frac{1}{4}$ .

Step 2

(a)(ii) Find the equation of line AB.

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Answer

To find the equation of line AB, we can use the point-slope form of the line equation:

$y - y_1 = m(x - x_1)$

Using point A (-4, 6) and the gradient $m = -\frac{1}{4}$ :

$y - 6 = -\frac{1}{4}(x + 4)$

Distributing the gradient:

$y - 6 = -\frac{1}{4}x - 1$

Now, add 6 to both sides to get it into slope-intercept form:

$y = -\frac{1}{4}x + 5$

Thus, the equation of line AB is:

$y = -\frac{1}{4}x + 5$

Step 3

(b) Write down the equation of the line parallel to line AB that passes through P.

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Answer

Since parallel lines have the same gradient, the gradient of the line passing through point P (0, -2) will also be $-\frac{1}{4}$ . Using the point-slope form again:

$y - y_1 = m(x - x_1)$

For point P (0, -2):

$y - (-2) = -\frac{1}{4}(x - 0)$

Simplifying this gives:

$y + 2 = -\frac{1}{4}x$

Subtracting 2 from both sides yields:

$y = -\frac{1}{4}x - 2$

Thus, the equation of the line parallel to line AB that passes through P is:

$y = -\frac{1}{4}x - 2$

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Point A has coordinates (-4, 6) and point B has coordinates (8, 3) - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

Worked Solution & Example Answer:Point A has coordinates (-4, 6) and point B has coordinates (8, 3) - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

(a)(i) Find the gradient of line AB.

(a)(ii) Find the equation of line AB.

(b) Write down the equation of the line parallel to line AB that passes through P.

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