Modelling with Straight Lines (Edexcel 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}

The midpoint formula uses which calculation?

Mean of the xx and yy coordinates

What is the midpoint of the segment with endpoints (2,4)(2, 4) and (8,10)(8, 10)?

(5,7)(5, 7)

What is the distance formula for a line segment?

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

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

55

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

y=−2x+11y = -2x + 11

For BB at (x,−2x+11)(x, -2x+11), distance from A(3,5)A(3,5) is 656\sqrt{5}. Which equation applies?

(x−3)2+(−2x+6)2=65\sqrt{(x-3)^2 + (-2x+6)^2} = 6\sqrt{5}

Solving x2−6x−27=0x^2 - 6x - 27 = 0 gives which values?

x=9x = 9 or x=−3x = -3

For line y=−2x+11y=-2x+11 with x=9x=9 or x=−3x=-3, what are the possible coordinates of BB?

(9,−7)(9, -7) and (−3,17)(-3, 17)

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