Modelling with Straight Lines (AQA A-Level Mathematics): Quizzes

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Modelling with Straight Lines
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What is the formula for the gradient mm of a line through (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)?

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Find the gradient of the line through (1,2)(1, 2) and (6,10)(6, 10).

85\frac{8}{5}

What is the midpoint of a line with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)?

(x1+x22,y1+y22)(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})

Find the midpoint of the line segment from (2,4)(2, 4) to (8,10)(8, 10).

(5,7)(5, 7)

What is the distance formula for a line segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)?

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

Find the length of the line segment from (0,0)(0, 0) to (3,4)(3, 4).

55

A line with gradient −2-2 passes through (3,5)(3, 5). What is its equation?

y=−2x+11y = -2x + 11

In the example, why are there two possible points BB?

BB can be on either side of AA on line ll

If BB is at (9,y)(9, y) on line y=−2x+11y = -2x + 11, what is yy?

−7-7

In the example, which quadratic equation is formed after simplification?

x2−6x−27=0x^2 - 6x - 27 = 0

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